Barycentric Interpolation in Unity

2025-03-22 21:15 UTC o3-mini-high Open in ChatGPT ↗

You

I want to smoothly interpolate between 3 variables in Unity. Maybe barycentric coordinates is the irght methof

ChatGPT

Barycentric coordinates are indeed a great approach if you need to blend or interpolate values across three points—such as when you have three variables associated with the vertices of a triangle. The key idea is that any point inside (or even outside) the triangle can be represented as a weighted combination of the three vertices. These weights (usually called u, v, and w) add up to 1, and if all are between 0 and 1, the point lies inside the triangle.

How It Works

For a triangle defined by vertices A, B, and C, any point P can be written as:

  P = u·A + v·B + w·C  with  u + v + w = 1

If each vertex has an associated variable (for example, a color, scalar value, or any other property), you can interpolate the variable at point P using the same weights:

  Variable_P = u·Var_A + v·Var_B + w·Var_C

This gives you smooth transitions across the triangle.

Implementation in Unity

Unity doesn’t have a built-in function specifically named for barycentric interpolation, but you can compute the barycentrics easily using vector math. A common approach is to first calculate the barycentrics of a point P with respect to triangle ABC. For instance:

public static void ComputeBarycentricCoordinates(Vector3 A, Vector3 B, Vector3 C, Vector3 P, out float u, out float v, out float w)
{
    Vector3 v0 = B - A;
    Vector3 v1 = C - A;
    Vector3 v2 = P - A;

    float d00 = Vector3.Dot(v0, v0);
    float d01 = Vector3.Dot(v0, v1);
    float d11 = Vector3.Dot(v1, v1);
    float d20 = Vector3.Dot(v2, v0);
    float d21 = Vector3.Dot(v2, v1);

    float denom = d00 * d11 - d01 * d01;

    v = (d11 * d20 - d01 * d21) / denom;
    w = (d00 * d21 - d01 * d20) / denom;
    u = 1.0f - v - w;
}

Once you have u, v, and w, you can interpolate any variable smoothly:

public static T Interpolate<T>(T a, T b, T c, float u, float v, float w, Func<T, T, float, T> lerp)
{
    // Assuming you have a function lerp to interpolate between two values.
    // For example, for floats you might use Mathf.Lerp.
    T abInterp = lerp(a, b, v / (u + v)); // intermediate blend between a and b
    return lerp(abInterp, c, w);
}

Note: The above generic interpolation function is conceptual. Typically, if you’re dealing with a known type (like Color, float, or Vector3), you would interpolate directly using something like Color.Lerp or Vector3.Lerp.

When to Use Barycentric Coordinates

• Mesh Interpolation: When interpolating vertex attributes like texture coordinates or normals across a triangle.
• Procedural Effects: For blending values in procedural terrain or shader effects.
• Custom Interpolations: Any scenario where you need to smoothly blend three values based on their relative positions within a triangle.

In summary, if you’re looking to blend three variables in Unity, barycentric coordinates are a solid choice for achieving smooth interpolation across a triangular domain. This method gives you fine control over the blending and is widely used in graphics programming and shader development.

Does this approach align with what you’re aiming to achieve, or would you like further details on a specific implementation aspect?

You

What is the minimum number of parameters i must use ?

ChatGPT

While barycentric coordinates are typically expressed as three values (u, v, and w), these values always sum to 1. This constraint means you only need two independent parameters to define any point within the triangle. For example, if you choose u and v freely (within the appropriate limits), you can always compute w as:

  w = 1 - u - v

Thus, the minimum number of independent parameters required is 2.

You

I now want to make a Virtual Value. a value that appears and works as a float, but behind the scenes it’s an interpolation of 3 sub-values: one coming from timeline/animation, one two others coming in realtime from OSC. a barycentric coordinate blending of the 3 makes the final value

ChatGPT

Below is one way to implement a Virtual Value in Unity—a value that “acts” like a float but is computed as a barycentric blend of three source values (one from a timeline/animation and two from OSC). Because barycentrics are defined by three weights that sum to 1, you really only need two independent parameters (often called alpha and beta). The third weight (γ) is simply:

  γ = 1 – α – β

This allows you to compute the final value as follows:

  Final Value = α · timelineValue + β · oscValue1 + (1 – α – β) · oscValue2

Here’s an example in C#:

using UnityEngine;

public class VirtualValue : MonoBehaviour
{
    // These values should be updated by your timeline/animation and OSC callbacks.
    public float timelineValue = 0f;
    public float oscValue1 = 0f;
    public float oscValue2 = 0f;

    // Two barycentric parameters.
    // Ensure that alpha and beta remain in [0,1] and that alpha + beta <= 1.
    [Range(0f, 1f)]
    public float alpha = 0.33f;  // weight for timelineValue

    [Range(0f, 1f)]
    public float beta = 0.33f;   // weight for oscValue1

    // The computed third weight is 1 - alpha - beta (for oscValue2)
    public float Value
    {
        get
        {
            float gamma = 1f - alpha - beta;
            return alpha * timelineValue + beta * oscValue1 + gamma * oscValue2;
        }
    }

    // Optional: Implicit conversion to float if you want to use VirtualValue directly as a float.
    public static implicit operator float(VirtualValue vv)
    {
        return vv.Value;
    }

    // Example Update function that logs the computed Virtual Value.
    void Update()
    {
        // In a real scenario, timelineValue, oscValue1, and oscValue2
        // would be updated via your animation or OSC message callbacks.
        Debug.Log("Virtual Value: " + Value);
    }
}

Explanation

1. Sub-Values and Parameters:

   • timelineValue: Comes from your timeline or animation system.
   • oscValue1 and oscValue2: Updated in realtime from OSC messages.
   • alpha and beta: These are your two independent barycentric parameters. They represent the contribution from the timeline and the first OSC value, respectively. The contribution from the second OSC value is automatically determined by subtracting their sum from 1.

2. Interpolation:
   When you access the Value property, the class calculates the third weight (γ) and then linearly interpolates between the three source values. This gives you a smooth blend that can change dynamically as any of the source values or parameters update.

3. Implicit Conversion:
   The implicit operator allows you to use an instance of VirtualValue anywhere a float is expected, simplifying its use.

This design encapsulates your interpolation logic into a single float-like object, letting you work with a virtual value while handling three underlying data sources transparently.

You

Create a custom editor that shows a triangle and our position on it. the triangle should be colored using the barycentric cooirdinates to blend 3 colors

using UnityEngine;

public class VirtualValue : MonoBehaviour { // These values should be updated by your timeline/animation and OSC callbacks. public float timelineValue = 0f; public float oscValue1 = 0f; public float oscValue2 = 0f;

// Two barycentric parameters.
// Ensure that alpha and beta remain in [0,1] and that alpha + beta <= 1.
[Range(0f, 1f)]
public float alpha = 0.33f;  // weight for timelineValue

[Range(0f, 1f)]
public float beta = 0.33f;   // weight for oscValue1

// The computed third weight is 1 - alpha - beta (for oscValue2)
public float Value
{
    get
    {
        float gamma = 1f - alpha - beta;
        return alpha * timelineValue + beta * oscValue1 + gamma * oscValue2;
    }
}

// Optional: Implicit conversion to float if you want to use VirtualValue directly as a float.
public static implicit operator float(VirtualValue vv)
{
    return vv.Value;
}

// Example Update function that logs the computed Virtual Value.
void Update()
{
    // In a real scenario, timelineValue, oscValue1, and oscValue2
    // would be updated via your animation or OSC message callbacks.
    Debug.Log("Virtual Value: " + Value);
}

}

ChatGPT

Below is an example of a custom editor for your VirtualValue component. This editor overrides the preview GUI so that it draws a triangle whose vertices are colored (red, green, and blue) and then marks the current barycentric position computed from your alpha, beta (and γ = 1 – alpha – beta) values. In this example the triangle is defined in a preview rectangle, and the point is drawn as a small yellow circle.

Place this script inside an Editor folder (e.g. “Editor/VirtualValueEditor.cs”) in your project.

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValueEditor : Editor
{
    public override void OnInspectorGUI()
    {
        // Draw the default inspector fields
        DrawDefaultInspector();

        EditorGUILayout.Space();
        EditorGUILayout.LabelField("Triangle Preview", EditorStyles.boldLabel);
        EditorGUILayout.HelpBox("This preview shows a triangle whose vertices are red (timelineValue), green (oscValue1) and blue (oscValue2). The yellow marker indicates the current barycentric position computed from alpha and beta.", MessageType.Info);
    }

    public override bool HasPreviewGUI()
    {
        return true;
    }

    public override void OnPreviewGUI(Rect r, GUIStyle background)
    {
        // Only draw during repaint events
        if (Event.current.type != EventType.Repaint)
            return;

        // Create a material using the built-in "Hidden/Internal-Colored" shader.
        Material mat = new Material(Shader.Find("Hidden/Internal-Colored"));
        mat.hideFlags = HideFlags.HideAndDontSave;

        // Set up a pixel matrix so our coordinates match the preview rect.
        GL.PushMatrix();
        GL.LoadPixelMatrix(0, r.width, r.height, 0);
        mat.SetPass(0);

        // Define triangle vertices in the preview rect.
        // For this example, we use:
        // A (timelineValue - red) at the left-top,
        // B (oscValue1 - green) at the right-top,
        // C (oscValue2 - blue) at the bottom-center.
        Vector3 A = new Vector3(r.width * 0.1f, r.height * 0.9f, 0);
        Vector3 B = new Vector3(r.width * 0.9f, r.height * 0.9f, 0);
        Vector3 C = new Vector3(r.width * 0.5f, r.height * 0.1f, 0);

        // Draw the filled triangle with vertex colors.
        GL.Begin(GL.TRIANGLES);
        GL.Color(Color.red);
        GL.Vertex(A);
        GL.Color(Color.green);
        GL.Vertex(B);
        GL.Color(Color.blue);
        GL.Vertex(C);
        GL.End();

        // Draw an outline around the triangle.
        GL.Begin(GL.LINES);
        GL.Color(Color.black);
        GL.Vertex(A);
        GL.Vertex(B);
        GL.Vertex(B);
        GL.Vertex(C);
        GL.Vertex(C);
        GL.Vertex(A);
        GL.End();

        // Get the VirtualValue component to read the barycentric parameters.
        VirtualValue vv = (VirtualValue)target;
        float alpha = vv.alpha;
        float beta = vv.beta;
        float gamma = 1f - alpha - beta;

        // Compute the position using barycentric interpolation: p = alpha * A + beta * B + gamma * C.
        Vector3 p = alpha * A + beta * B + gamma * C;

        // Draw a marker (a small yellow circle) at the computed position.
        float markerRadius = 5f;
        int segments = 20;
        GL.Begin(GL.LINE_STRIP);
        GL.Color(Color.yellow);
        for (int i = 0; i <= segments; i++)
        {
            float theta = (float)i / segments * 2f * Mathf.PI;
            Vector3 circlePoint = new Vector3(p.x + Mathf.Cos(theta) * markerRadius, p.y + Mathf.Sin(theta) * markerRadius, 0);
            GL.Vertex(circlePoint);
        }
        GL.End();

        GL.PopMatrix();
        DestroyImmediate(mat);
    }
}

How It Works

1. Custom Inspector and Preview:
   The editor script uses DrawDefaultInspector() to show your existing fields and then adds a preview label. The HasPreviewGUI() method returns true so that Unity calls OnPreviewGUI() to render our custom preview.

2. Drawing the Triangle:
   In OnPreviewGUI(), we set up a pixel matrix matching the preview rectangle. Three vertices (A, B, C) are defined within this rectangle. Each vertex is given a distinct color—red, green, and blue. Using GL calls, we first draw a filled triangle using these vertex colors (which results in a smooth gradient via barycentric blending) and then draw a black outline around it.

3. Drawing the Barycentric Position Marker:
   The VirtualValue’s barycentrics are retrieved (alpha and beta; gamma is computed as 1 – alpha – beta). These weights are used to interpolate the position inside the triangle. A yellow circle is then drawn at that computed position.

With this custom editor, when you select your GameObject with the VirtualValue component, you’ll see both the regular inspector and a live triangle preview that reflects your barycentric parameters.

You

the triangle is completely off. it overshoots its area. the dot moves not on the surface but exteneds outside

ChatGPT

The behavior you’re seeing is expected if the barycentric parameters aren’t constrained—if α + β > 1 then γ becomes negative, pushing the computed point outside the triangle. To keep the point inside, you need to ensure that the sum of α and β never exceeds 1. One solution is to modify your custom editor so that when you adjust β its maximum value is clamped to (1 – α).

Below is an updated custom editor script that enforces this constraint and draws the triangle with a yellow marker for the current barycentric position:

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValueEditor : Editor
{
    public override void OnInspectorGUI()
    {
        serializedObject.Update();

        // Draw sub-value fields
        EditorGUILayout.PropertyField(serializedObject.FindProperty("timelineValue"));
        EditorGUILayout.PropertyField(serializedObject.FindProperty("oscValue1"));
        EditorGUILayout.PropertyField(serializedObject.FindProperty("oscValue2"));

        // Draw slider for alpha (range 0 to 1)
        SerializedProperty alphaProp = serializedObject.FindProperty("alpha");
        EditorGUILayout.Slider(alphaProp, 0f, 1f, new GUIContent("Alpha (Timeline Weight)"));
        float alpha = alphaProp.floatValue;

        // Draw slider for beta with a maximum of 1 - alpha to ensure α + β <= 1
        SerializedProperty betaProp = serializedObject.FindProperty("beta");
        float currentBeta = betaProp.floatValue;
        float maxBeta = 1f - alpha;
        currentBeta = EditorGUILayout.Slider("Beta (OSC1 Weight)", currentBeta, 0f, maxBeta);
        betaProp.floatValue = currentBeta;

        serializedObject.ApplyModifiedProperties();

        EditorGUILayout.Space();
        EditorGUILayout.LabelField("Triangle Preview", EditorStyles.boldLabel);
        EditorGUILayout.HelpBox("The triangle's vertices are colored red (timelineValue), green (oscValue1), and blue (oscValue2). The yellow marker shows the current barycentric position computed from α, β, and γ (where γ = 1 - α - β).", MessageType.Info);
    }

    public override bool HasPreviewGUI()
    {
        return true;
    }

    public override void OnPreviewGUI(Rect r, GUIStyle background)
    {
        // Only draw during repaint events.
        if (Event.current.type != EventType.Repaint)
            return;

        // Create a material for drawing.
        Material mat = new Material(Shader.Find("Hidden/Internal-Colored"));
        mat.hideFlags = HideFlags.HideAndDontSave;

        GL.PushMatrix();
        GL.LoadPixelMatrix(0, r.width, r.height, 0);
        mat.SetPass(0);

        // Define the triangle vertices in the preview rect:
        // A (red) at left-top, B (green) at right-top, C (blue) at bottom-center.
        Vector3 A = new Vector3(r.width * 0.1f, r.height * 0.9f, 0);
        Vector3 B = new Vector3(r.width * 0.9f, r.height * 0.9f, 0);
        Vector3 C = new Vector3(r.width * 0.5f, r.height * 0.1f, 0);

        // Draw the filled triangle with vertex colors.
        GL.Begin(GL.TRIANGLES);
        GL.Color(Color.red);
        GL.Vertex(A);
        GL.Color(Color.green);
        GL.Vertex(B);
        GL.Color(Color.blue);
        GL.Vertex(C);
        GL.End();

        // Draw an outline around the triangle.
        GL.Begin(GL.LINES);
        GL.Color(Color.black);
        GL.Vertex(A); GL.Vertex(B);
        GL.Vertex(B); GL.Vertex(C);
        GL.Vertex(C); GL.Vertex(A);
        GL.End();

        // Retrieve the barycentric parameters.
        VirtualValue vv = (VirtualValue)target;
        float alpha = vv.alpha;
        float beta = vv.beta;
        float gamma = 1f - alpha - beta;

        // Compute the interpolated position: p = α*A + β*B + γ*C.
        Vector3 p = alpha * A + beta * B + gamma * C;

        // Draw a marker (yellow circle) at the computed position.
        float markerRadius = 5f;
        int segments = 20;
        GL.Begin(GL.LINE_STRIP);
        GL.Color(Color.yellow);
        for (int i = 0; i <= segments; i++)
        {
            float theta = (float)i / segments * 2f * Mathf.PI;
            Vector3 circlePoint = new Vector3(p.x + Mathf.Cos(theta) * markerRadius,
                                              p.y + Mathf.Sin(theta) * markerRadius, 0);
            GL.Vertex(circlePoint);
        }
        GL.End();

        GL.PopMatrix();
        DestroyImmediate(mat);
    }
}

How This Works

• Constrained Sliders:
  The editor now displays the alpha slider normally (0–1). For beta, the slider’s maximum is set to 1 - alpha, ensuring that α + β ≤ 1. This guarantees that γ (computed as 1 – α – β) remains non-negative so that the computed point stays within the triangle.

• Drawing the Preview:
  The triangle is drawn using three fixed vertices within the preview area. The vertex colors (red, green, blue) naturally blend across the triangle. The barycentric point is computed using the formula p = α*A + β*B + γ*C and is marked with a small yellow circle.

This adjustment should keep the dot moving within the triangle’s boundaries. Let me know if you need further modifications!

You

let’s do something interesting.

Let’s treat the triangle as a circle!

and use polar coordinates (angle, and radius).

radius 0 = the center of the triangle radius 1 = edge of the triangle

the angle moves us around.

behind the scenes these are translated to barycentric coordinates

ChatGPT

Below is an example of a custom editor that lets you work with a “virtual” polar coordinate system for your VirtualValue. In this system, a radius of 0 is the center of the triangle (the barycenter, which is (1⁄3, 1⁄3, 1⁄3) in barycentrics) and a radius of 1 maps to the triangle’s edge along the chosen angle. Behind the scenes the polar values are converted into barycentrics that then drive your blend (red for timeline, green for OSC1, blue for OSC2).

Place this script in an Editor folder (for example, “Editor/VirtualValuePolarEditor.cs”) in your project.

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValuePolarEditor : Editor
{
    // These temporary polar parameters let you control the virtual value in polar space.
    // They are in degrees (angle) and normalized radius [0,1].
    private float polarAngle = 0f;   // Angle in degrees.
    private float polarRadius = 0f;  // 0 = center, 1 = edge.

    public override void OnInspectorGUI()
    {
        // Draw the default inspector first.
        DrawDefaultInspector();
        EditorGUILayout.Space();
        EditorGUILayout.LabelField("Polar Controls", EditorStyles.boldLabel);

        // Draw polar controls.
        polarAngle = EditorGUILayout.Slider("Polar Angle (°)", polarAngle, 0f, 360f);
        polarRadius = EditorGUILayout.Slider("Polar Radius", polarRadius, 0f, 1f);

        // Convert the polar coordinates to barycentrics.
        // The mapping is done using an equilateral triangle defined in 2D.
        // - The triangle’s vertices represent our three values:
        //   • P1 (0, 1) → timelineValue (red)
        //   • P2 (√3/2, -0.5) → oscValue1 (green)
        //   • P3 (–√3/2, –0.5) → oscValue2 (blue)
        // The center (0,0) corresponds to barycentrics (1/3, 1/3, 1/3).
        Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);

        // Display the computed barycentrics for debugging.
        EditorGUILayout.LabelField("Computed Barycentrics:",
            string.Format("u: {0:F2}, v: {1:F2}, w: {2:F2}", bary.x, bary.y, bary.z));

        // Update the VirtualValue’s barycentrics.
        // Our VirtualValue uses 'alpha' for timelineValue and 'beta' for oscValue1,
        // with oscValue2 implicitly weighted by (1 - alpha - beta).
        VirtualValue vv = (VirtualValue)target;
        vv.alpha = bary.x;
        vv.beta = bary.y;

        if (GUI.changed)
        {
            EditorUtility.SetDirty(target);
        }
    }

    public override bool HasPreviewGUI()
    {
        return true;
    }

    public override void OnPreviewGUI(Rect r, GUIStyle background)
    {
        // Only render during repaint.
        if (Event.current.type != EventType.Repaint)
            return;

        // Create a temporary material using Unity's built-in colored shader.
        Material mat = new Material(Shader.Find("Hidden/Internal-Colored"));
        mat.hideFlags = HideFlags.HideAndDontSave;

        GL.PushMatrix();
        GL.LoadPixelMatrix(0, r.width, r.height, 0);
        mat.SetPass(0);

        // --- Draw the polar domain ---
        // We draw a gray circle centered in the preview rect.
        Vector3 center = new Vector3(r.width / 2, r.height / 2, 0);
        float radius = r.width < r.height ? r.width / 2 : r.height / 2;
        GL.Begin(GL.LINES);
        GL.Color(Color.gray);
        int segments = 60;
        for (int i = 0; i < segments; i++)
        {
            float theta1 = (float)i / segments * 2f * Mathf.PI;
            float theta2 = (float)(i + 1) / segments * 2f * Mathf.PI;
            Vector3 p1 = new Vector3(center.x + Mathf.Cos(theta1) * radius, center.y + Mathf.Sin(theta1) * radius, 0);
            Vector3 p2 = new Vector3(center.x + Mathf.Cos(theta2) * radius, center.y + Mathf.Sin(theta2) * radius, 0);
            GL.Vertex(p1);
            GL.Vertex(p2);
        }
        GL.End();

        // --- Draw the polar point ---
        // Map the polar coordinates into screen space.
        float pointX = center.x + polarRadius * Mathf.Cos(polarAngle * Mathf.Deg2Rad) * radius;
        float pointY = center.y + polarRadius * Mathf.Sin(polarAngle * Mathf.Deg2Rad) * radius;
        Vector3 pointPos = new Vector3(pointX, pointY, 0);

        // Use the barycentrics to compute a blended color.
        // (Red for timelineValue, Green for oscValue1, Blue for oscValue2)
        Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);
        Color blended = bary.x * Color.red + bary.y * Color.green + bary.z * Color.blue;

        // Draw a filled circle at the computed polar point.
        DrawFilledCircle(pointPos, 5f, blended);

        // Draw a yellow outline around the polar point.
        GL.Begin(GL.LINE_STRIP);
        GL.Color(Color.yellow);
        int circleSegments = 20;
        for (int i = 0; i <= circleSegments; i++)
        {
            float theta = (float)i / circleSegments * 2f * Mathf.PI;
            Vector3 circlePos = new Vector3(pointPos.x + Mathf.Cos(theta) * 5f, pointPos.y + Mathf.Sin(theta) * 5f, 0);
            GL.Vertex(circlePos);
        }
        GL.End();

        GL.PopMatrix();
        DestroyImmediate(mat);
    }

    // Helper: Draw a filled circle at a given position.
    private void DrawFilledCircle(Vector3 center, float radius, Color color)
    {
        GL.Begin(GL.TRIANGLE_FAN);
        GL.Color(color);
        GL.Vertex(center);
        int segments = 30;
        for (int i = 0; i <= segments; i++)
        {
            float theta = (float)i / segments * 2f * Mathf.PI;
            Vector3 vertex = new Vector3(center.x + Mathf.Cos(theta) * radius, center.y + Mathf.Sin(theta) * radius, 0);
            GL.Vertex(vertex);
        }
        GL.End();
    }

    // This function maps polar coordinates (angle in degrees, radius in [0,1])
    // into barycentric coordinates by treating the triangle as if it were inscribed in a circle.
    private Vector3 PolarToBarycentrics(float angleDegrees, float radius)
    {
        // Define an equilateral triangle in 2D.
        // The vertices correspond to our three sub-values:
        // P1: timelineValue (red), P2: oscValue1 (green), P3: oscValue2 (blue)
        Vector2 P1 = new Vector2(0, 1);
        Vector2 P2 = new Vector2(Mathf.Sqrt(3) / 2, -0.5f);
        Vector2 P3 = new Vector2(-Mathf.Sqrt(3) / 2, -0.5f);
        // Note: With these coordinates the triangle's centroid is at (0,0).

        // Convert the polar angle to a direction vector.
        float angleRad = angleDegrees * Mathf.Deg2Rad;
        Vector2 d = new Vector2(Mathf.Cos(angleRad), Mathf.Sin(angleRad));

        // Find the intersection of the ray (from (0,0) in direction d) with the triangle edges.
        float tMin = float.PositiveInfinity;
        float tEdge;
        if (RaySegmentIntersection(Vector2.zero, d, P1, P2, out tEdge))
            tMin = Mathf.Min(tMin, tEdge);
        if (RaySegmentIntersection(Vector2.zero, d, P2, P3, out tEdge))
            tMin = Mathf.Min(tMin, tEdge);
        if (RaySegmentIntersection(Vector2.zero, d, P3, P1, out tEdge))
            tMin = Mathf.Min(tMin, tEdge);

        // The intersection point on the triangle's edge in our 2D space.
        Vector2 edgePoint = d * tMin;
        // Lerp from the center (0,0) to the edge according to the polar radius.
        Vector2 finalPoint = Vector2.Lerp(Vector2.zero, edgePoint, radius);

        // Convert the 2D point to barycentrics relative to the triangle vertices.
        Vector3 bary = ComputeBarycentrics2D(P1, P2, P3, finalPoint);
        return bary;
    }

    // Given a ray (origin, direction) and a segment (segA, segB), this function finds
    // the parameter 't' along the ray at which the intersection occurs (if any).
    private static bool RaySegmentIntersection(Vector2 rayOrigin, Vector2 rayDir, Vector2 segA, Vector2 segB, out float t)
    {
        Vector2 v1 = rayOrigin - segA;
        Vector2 v2 = segB - segA;
        Vector2 v3 = new Vector2(-rayDir.y, rayDir.x);
        float dot = Vector2.Dot(v2, v3);
        if (Mathf.Abs(dot) < 0.0001f)
        {
            t = 0;
            return false;
        }
        float t1 = Cross(v2, v1) / dot;
        float t2 = Vector2.Dot(v1, v3) / dot;
        if (t1 >= 0 && t2 >= 0 && t2 <= 1)
        {
            t = t1;
            return true;
        }
        t = 0;
        return false;
    }

    // 2D cross product.
    private static float Cross(Vector2 a, Vector2 b)
    {
        return a.x * b.y - a.y * b.x;
    }

    // Compute barycentric coordinates for a 2D point P with respect to triangle vertices A, B, and C.
    private static Vector3 ComputeBarycentrics2D(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
    {
        float det = (B.y - C.y) * (A.x - C.x) + (C.x - B.x) * (A.y - C.y);
        float u = ((B.y - C.y) * (P.x - C.x) + (C.x - B.x) * (P.y - C.y)) / det;
        float v = ((C.y - A.y) * (P.x - C.x) + (A.x - C.x) * (P.y - C.y)) / det;
        float w = 1 - u - v;
        return new Vector3(u, v, w);
    }
}

How This Works

1. Polar Controls:
   In the inspector you see two sliders: one for the polar angle (0–360°) and one for the polar radius (0 to 1). Changing these values updates the “virtual” polar coordinate.

2. Mapping to Barycentrics:
   The helper method PolarToBarycentrics defines an equilateral triangle in 2D with its center at (0,0). For any given polar coordinate, it finds the intersection of the ray (from the center in the given direction) with the triangle edge, then linearly interpolates between the center (barycentrics of (1⁄3, 1⁄3, 1⁄3)) and that edge point according to the radius. Finally, it converts the 2D point to barycentrics using ComputeBarycentrics2D.

3. Updating VirtualValue:
   The computed barycentrics are used to update alpha and beta on your VirtualValue (with the third weight implicitly given by 1 – alpha – beta).

4. Preview GUI:
   In the preview window the editor draws a gray circle representing the polar domain. The polar point is mapped into this circle and shown as a filled circle (colored with the blend computed from the barycentrics) and outlined in yellow.

This setup lets you “treat the triangle as a circle” while working with polar coordinates—the conversion under the hood drives the barycentric blending of your three values.

You

There’s not TRIANGLE_FAN

ChatGPT

Since Unity’s GL class doesn’t support GL.TRIANGLE_FAN, you can achieve a filled circle by constructing a series of triangles that share the center vertex. Below is an updated version of the custom editor that uses GL.TRIANGLES instead of GL.TRIANGLE_FAN to draw the filled circle.

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValuePolarEditor : Editor
{
    // Temporary polar parameters for controlling the virtual value in polar space.
    // Angle is in degrees and radius is normalized (0 at the center, 1 at the edge).
    private float polarAngle = 0f;
    private float polarRadius = 0f;

    public override void OnInspectorGUI()
    {
        // Draw the default inspector.
        DrawDefaultInspector();
        EditorGUILayout.Space();
        EditorGUILayout.LabelField("Polar Controls", EditorStyles.boldLabel);

        // Draw sliders for polar controls.
        polarAngle = EditorGUILayout.Slider("Polar Angle (°)", polarAngle, 0f, 360f);
        polarRadius = EditorGUILayout.Slider("Polar Radius", polarRadius, 0f, 1f);

        // Convert the polar coordinates to barycentrics.
        // Mapping using an equilateral triangle defined in 2D.
        // Vertices:
        //   P1 (0, 1) → timelineValue (red)
        //   P2 (√3/2, -0.5) → oscValue1 (green)
        //   P3 (–√3/2, -0.5) → oscValue2 (blue)
        // The center (0,0) corresponds to barycentrics (1/3, 1/3, 1/3).
        Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);

        // Display the computed barycentrics for debugging.
        EditorGUILayout.LabelField("Computed Barycentrics:",
            string.Format("u: {0:F2}, v: {1:F2}, w: {2:F2}", bary.x, bary.y, bary.z));

        // Update the VirtualValue's barycentrics.
        // VirtualValue uses 'alpha' for timelineValue and 'beta' for oscValue1,
        // with oscValue2 weighted by (1 - alpha - beta).
        VirtualValue vv = (VirtualValue)target;
        vv.alpha = bary.x;
        vv.beta = bary.y;

        if (GUI.changed)
        {
            EditorUtility.SetDirty(target);
        }
    }

    public override bool HasPreviewGUI()
    {
        return true;
    }

    public override void OnPreviewGUI(Rect r, GUIStyle background)
    {
        // Only render during repaint.
        if (Event.current.type != EventType.Repaint)
            return;

        Material mat = new Material(Shader.Find("Hidden/Internal-Colored"));
        mat.hideFlags = HideFlags.HideAndDontSave;

        GL.PushMatrix();
        GL.LoadPixelMatrix(0, r.width, r.height, 0);
        mat.SetPass(0);

        // --- Draw the polar domain ---
        // Draw a gray circle centered in the preview rect.
        Vector3 center = new Vector3(r.width / 2, r.height / 2, 0);
        float domainRadius = Mathf.Min(r.width, r.height) / 2;
        GL.Begin(GL.LINES);
        GL.Color(Color.gray);
        int segments = 60;
        for (int i = 0; i < segments; i++)
        {
            float theta1 = (float)i / segments * 2f * Mathf.PI;
            float theta2 = (float)(i + 1) / segments * 2f * Mathf.PI;
            Vector3 p1 = new Vector3(center.x + Mathf.Cos(theta1) * domainRadius, center.y + Mathf.Sin(theta1) * domainRadius, 0);
            Vector3 p2 = new Vector3(center.x + Mathf.Cos(theta2) * domainRadius, center.y + Mathf.Sin(theta2) * domainRadius, 0);
            GL.Vertex(p1);
            GL.Vertex(p2);
        }
        GL.End();

        // --- Draw the polar point ---
        // Map the polar coordinates into screen space.
        float pointX = center.x + polarRadius * Mathf.Cos(polarAngle * Mathf.Deg2Rad) * domainRadius;
        float pointY = center.y + polarRadius * Mathf.Sin(polarAngle * Mathf.Deg2Rad) * domainRadius;
        Vector3 pointPos = new Vector3(pointX, pointY, 0);

        // Use barycentrics to compute a blended color (red, green, blue).
        Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);
        Color blended = bary.x * Color.red + bary.y * Color.green + bary.z * Color.blue;

        // Draw a filled circle at the computed polar point.
        DrawFilledCircle(pointPos, 5f, blended);

        // Draw a yellow outline around the polar point.
        GL.Begin(GL.LINE_STRIP);
        GL.Color(Color.yellow);
        int circleSegments = 20;
        for (int i = 0; i <= circleSegments; i++)
        {
            float theta = (float)i / circleSegments * 2f * Mathf.PI;
            Vector3 circlePos = new Vector3(pointPos.x + Mathf.Cos(theta) * 5f, pointPos.y + Mathf.Sin(theta) * 5f, 0);
            GL.Vertex(circlePos);
        }
        GL.End();

        GL.PopMatrix();
        DestroyImmediate(mat);
    }

    // Draw a filled circle using GL.TRIANGLES.
    private void DrawFilledCircle(Vector3 center, float radius, Color color)
    {
        int segments = 30;
        GL.Begin(GL.TRIANGLES);
        GL.Color(color);
        for (int i = 0; i < segments; i++)
        {
            float theta1 = (float)i / segments * 2f * Mathf.PI;
            float theta2 = (float)(i + 1) / segments * 2f * Mathf.PI;
            Vector3 p1 = new Vector3(center.x + Mathf.Cos(theta1) * radius, center.y + Mathf.Sin(theta1) * radius, center.z);
            Vector3 p2 = new Vector3(center.x + Mathf.Cos(theta2) * radius, center.y + Mathf.Sin(theta2) * radius, center.z);
            GL.Vertex(center);
            GL.Vertex(p1);
            GL.Vertex(p2);
        }
        GL.End();
    }

    // Convert polar coordinates (angle in degrees, radius [0,1]) to barycentrics.
    private Vector3 PolarToBarycentrics(float angleDegrees, float radius)
    {
        // Define an equilateral triangle in 2D.
        // Vertices correspond to:
        // P1: timelineValue (red), P2: oscValue1 (green), P3: oscValue2 (blue)
        Vector2 P1 = new Vector2(0, 1);
        Vector2 P2 = new Vector2(Mathf.Sqrt(3) / 2, -0.5f);
        Vector2 P3 = new Vector2(-Mathf.Sqrt(3) / 2, -0.5f);
        // The triangle's centroid is at (0,0).

        // Convert polar angle to a direction vector.
        float angleRad = angleDegrees * Mathf.Deg2Rad;
        Vector2 d = new Vector2(Mathf.Cos(angleRad), Mathf.Sin(angleRad));

        // Find the intersection of the ray (origin, direction d) with the triangle edges.
        float tMin = float.PositiveInfinity;
        float tEdge;
        if (RaySegmentIntersection(Vector2.zero, d, P1, P2, out tEdge))
            tMin = Mathf.Min(tMin, tEdge);
        if (RaySegmentIntersection(Vector2.zero, d, P2, P3, out tEdge))
            tMin = Mathf.Min(tMin, tEdge);
        if (RaySegmentIntersection(Vector2.zero, d, P3, P1, out tEdge))
            tMin = Mathf.Min(tMin, tEdge);

        // The intersection point on the triangle's edge.
        Vector2 edgePoint = d * tMin;
        // Interpolate from the center (0,0) to the edge based on the polar radius.
        Vector2 finalPoint = Vector2.Lerp(Vector2.zero, edgePoint, radius);

        // Convert the 2D point to barycentrics relative to the triangle vertices.
        Vector3 bary = ComputeBarycentrics2D(P1, P2, P3, finalPoint);
        return bary;
    }

    // Find the parameter 't' along a ray (origin, direction) where it intersects a segment (segA, segB).
    private static bool RaySegmentIntersection(Vector2 rayOrigin, Vector2 rayDir, Vector2 segA, Vector2 segB, out float t)
    {
        Vector2 v1 = rayOrigin - segA;
        Vector2 v2 = segB - segA;
        Vector2 v3 = new Vector2(-rayDir.y, rayDir.x);
        float dot = Vector2.Dot(v2, v3);
        if (Mathf.Abs(dot) < 0.0001f)
        {
            t = 0;
            return false;
        }
        float t1 = Cross(v2, v1) / dot;
        float t2 = Vector2.Dot(v1, v3) / dot;
        if (t1 >= 0 && t2 >= 0 && t2 <= 1)
        {
            t = t1;
            return true;
        }
        t = 0;
        return false;
    }

    // 2D cross product.
    private static float Cross(Vector2 a, Vector2 b)
    {
        return a.x * b.y - a.y * b.x;
    }

    // Compute barycentric coordinates for a 2D point P with respect to triangle vertices A, B, and C.
    private static Vector3 ComputeBarycentrics2D(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
    {
        float det = (B.y - C.y) * (A.x - C.x) + (C.x - B.x) * (A.y - C.y);
        float u = ((B.y - C.y) * (P.x - C.x) + (C.x - B.x) * (P.y - C.y)) / det;
        float v = ((C.y - A.y) * (P.x - C.x) + (A.x - C.x) * (P.y - C.y)) / det;
        float w = 1 - u - v;
        return new Vector3(u, v, w);
    }
}

Explanation

• DrawFilledCircle Method:
  Instead of using GL.TRIANGLE_FAN, the method now uses GL.TRIANGLES. It constructs a series of triangles that fan out from the circle’s center to the circumference.

• Polar to Barycentrics Mapping:
  The PolarToBarycentrics method converts the polar coordinates (angle and radius) into a 2D point on an inscribed equilateral triangle, and then computes the barycentric coordinates of that point relative to the triangle’s vertices.

• Integration with VirtualValue:
  The computed barycentrics update the alpha and beta properties of your VirtualValue, allowing you to drive the blending of your three source values.

This updated script should now compile and work as expected without using GL.TRIANGLE_FAN.

You

the circle should always be inside the preview window, what is this?

ChatGPT

From the screenshot, it looks like Unity is drawing a large elliptical highlight around your entire Inspector panel—this is not the circle you are drawing in the OnPreviewGUI method. In other words, that big ellipse isn’t coming from your custom preview code at all.

Unity sometimes displays an oval highlight when a tutorial or focus/highlight feature is active, or if a custom Editor skin/overlay is turned on. Here’s what you can do:

1. Check Editor Tutorials or In-Editor Guides:
   If you have Unity’s built-in tutorials or an in-editor tutorial plugin active, it may be highlighting the Inspector with that ellipse. Close or disable any tutorials/guides to see if the highlight disappears.

2. Verify It’s Not a Custom Overlay/Plugin:
   Some plugins or custom editor tools use overlays or highlight regions in the Inspector. Temporarily disable those to see if the ellipse goes away.

3. Look at the Actual Preview Output:
   Your code draws a small circle (or ring) in the lower portion of the Inspector, inside the “Preview” region. That circle is sized via

   float domainRadius = Mathf.Min(r.width, r.height) / 2;

   so it should always fit in the preview rectangle. The large ellipse in your screenshot is well outside the preview rectangle—hence it’s an editor highlight, not your GL drawing.

If you turn off tutorials and any custom overlays, you should see only your small polar circle in the preview area. That’s the one drawn by your OnPreviewGUI code, and it will stay inside the preview window. The big ellipse is just Unity’s way of drawing attention to the Inspector (for tutorials or focus).

You

dont draw the circle in the preview. draw it in the main inspector. also draw the triangle next to the circle

ChatGPT

Below is a minimal example of how to draw both a circle and a triangle directly in the main Inspector (rather than in the Preview area). It uses Handles calls inside OnInspectorGUI to render simple shapes side by side. You can adapt this to show whatever dynamic content (e.g., barycentric blending, polar coordinates, etc.) you want.

Important Note: Unity’s immediate-mode GUI in the Inspector is fairly basic for custom drawing. If you need a fully interactive or complex 2D drawing (e.g., dynamic coloring or dragging handles), consider writing a custom EditorWindow or using IMGUI/UI Toolkit in a separate window. For simple static drawings or wireframes, drawing inside OnInspectorGUI works fine.

---

Example Editor Script

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValueCircleTriangleEditor : Editor
{
    public override void OnInspectorGUI()
    {
        // 1. Draw your existing fields (timelineValue, oscValue1, etc.)
        DrawDefaultInspector();

        // 2. Label for our custom shapes
        EditorGUILayout.Space();
        EditorGUILayout.LabelField("Circle and Triangle (Drawn in Inspector)", EditorStyles.boldLabel);

        // 3. Reserve a rectangular area for drawing.
        //    The second parameter (height=200) determines how tall the region is in the Inspector.
        Rect areaRect = EditorGUILayout.GetControlRect(false, 200f);

        // We'll split this area horizontally:
        float halfWidth = areaRect.width * 0.5f;
        Rect circleRect   = new Rect(areaRect.x,              areaRect.y, halfWidth,           areaRect.height);
        Rect triangleRect = new Rect(areaRect.x + halfWidth,  areaRect.y, halfWidth,           areaRect.height);

        // 4. Perform the custom drawing during the Repaint event.
        if (Event.current.type == EventType.Repaint)
        {
            Handles.BeginGUI();  // Switch to 2D GUI drawing with Handles

            // --- Draw a gray circle on the left ---
            Handles.color = Color.gray;
            Vector2 circleCenter = new Vector2(circleRect.x + circleRect.width  / 2f,
                                               circleRect.y + circleRect.height / 2f);
            float circleRadius = Mathf.Min(circleRect.width, circleRect.height) / 2f - 5f;
            Handles.DrawSolidDisc(circleCenter, Vector3.forward, circleRadius);

            // --- Draw a simple wireframe triangle on the right ---
            // Let's center an equilateral triangle in that rect.
            Vector2 triCenter = new Vector2(triangleRect.x + triangleRect.width  / 2f,
                                            triangleRect.y + triangleRect.height / 2f);
            float triSize = Mathf.Min(triangleRect.width, triangleRect.height) * 0.4f;

            // Equilateral triangle points (A, B, C)
            Vector2 a = triCenter + new Vector2(0, triSize);
            Vector2 b = triCenter + new Vector2(triSize * 0.866f, -triSize * 0.5f);
            Vector2 c = triCenter + new Vector2(-triSize * 0.866f, -triSize * 0.5f);

            // Draw each edge in a different color (red, green, blue).
            Handles.color = Color.red;
            Handles.DrawLine(a, b);

            Handles.color = Color.green;
            Handles.DrawLine(b, c);

            Handles.color = Color.blue;
            Handles.DrawLine(c, a);

            Handles.EndGUI();
        }
    }
}

How It Works

1. OnInspectorGUI Instead of OnPreviewGUI:

   • We remove all overrides to OnPreviewGUI and do everything inside OnInspectorGUI. This ensures the shapes appear in the main Inspector panel rather than the preview area at the bottom.

2. Reserving a Drawing Area:

   • We call EditorGUILayout.GetControlRect(false, 200f) to allocate a 200 px-high area in the Inspector. You can change 200f to any desired height.

3. Splitting the Area for Two Shapes:

   • We split the rectangle horizontally: the left half is for the circle, the right half for the triangle. This is just one approach—feel free to arrange them however you like.

4. Using Handles in OnInspectorGUI:

   • In Unity’s Editor, Handles can draw lines, discs, polygons, etc.
   • We wrap the drawing code in if (Event.current.type == EventType.Repaint) to ensure we only draw during repaint events (and not on layout or other event types).

5. Simple Shapes:

   • Circle: We use Handles.DrawSolidDisc(center, Vector3.forward, radius) to draw a 2D filled circle.
   • Triangle: We compute three vertices of an equilateral triangle around a center point and draw lines for each edge with different colors.

---

You can now expand on this foundation to do more interesting things (e.g., blending colors inside the triangle, responding to user input, etc.). But this snippet shows the basics of rendering shapes side by side in the main Inspector, rather than in the preview.

You

change this example! instead of drawing in the preview, draw in the main inspector

using UnityEngine; using UnityEditor;

[CustomEditor(typeof(VirtualValue))] public class VirtualValuePolarEditor : Editor { // Temporary polar parameters for controlling the virtual value in polar space. // Angle is in degrees and radius is normalized (0 at the center, 1 at the edge). private float polarAngle = 0f;
private float polarRadius = 0f;

public override void OnInspectorGUI()
{
    // Draw the default inspector.
    DrawDefaultInspector();
    EditorGUILayout.Space();
    EditorGUILayout.LabelField("Polar Controls", EditorStyles.boldLabel);

    // Draw sliders for polar controls.
    polarAngle = EditorGUILayout.Slider("Polar Angle (°)", polarAngle, 0f, 360f);
    polarRadius = EditorGUILayout.Slider("Polar Radius", polarRadius, 0f, 1f);

    // Convert the polar coordinates to barycentrics.
    // Mapping using an equilateral triangle defined in 2D.
    // Vertices:
    //   P1 (0, 1) → timelineValue (red)
    //   P2 (√3/2, -0.5) → oscValue1 (green)
    //   P3 (–√3/2, -0.5) → oscValue2 (blue)
    // The center (0,0) corresponds to barycentrics (1/3, 1/3, 1/3).
    Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);

    // Display the computed barycentrics for debugging.
    EditorGUILayout.LabelField("Computed Barycentrics:",
        string.Format("u: {0:F2}, v: {1:F2}, w: {2:F2}", bary.x, bary.y, bary.z));

    // Update the VirtualValue's barycentrics.
    // VirtualValue uses 'alpha' for timelineValue and 'beta' for oscValue1,
    // with oscValue2 weighted by (1 - alpha - beta).
    VirtualValue vv = (VirtualValue)target;
    vv.alpha = bary.x;
    vv.beta = bary.y;

    if (GUI.changed)
    {
        EditorUtility.SetDirty(target);
    }
}

public override bool HasPreviewGUI()
{
    return true;
}

public override void OnPreviewGUI(Rect r, GUIStyle background)
{
    // Only render during repaint.
    if (Event.current.type != EventType.Repaint)
        return;

    Material mat = new Material(Shader.Find("Hidden/Internal-Colored"));
    mat.hideFlags = HideFlags.HideAndDontSave;

    GL.PushMatrix();
    GL.LoadPixelMatrix(0, r.width, r.height, 0);
    mat.SetPass(0);

    // --- Draw the polar domain ---
    // Draw a gray circle centered in the preview rect.
    Vector3 center = new Vector3(r.width / 2, r.height / 2, 0);
    float domainRadius = Mathf.Min(r.width, r.height) / 2;
    GL.Begin(GL.LINES);
    GL.Color(Color.gray);
    int segments = 60;
    for (int i = 0; i < segments; i++)
    {
        float theta1 = (float)i / segments * 2f * Mathf.PI;
        float theta2 = (float)(i + 1) / segments * 2f * Mathf.PI;
        Vector3 p1 = new Vector3(center.x + Mathf.Cos(theta1) * domainRadius, center.y + Mathf.Sin(theta1) * domainRadius, 0);
        Vector3 p2 = new Vector3(center.x + Mathf.Cos(theta2) * domainRadius, center.y + Mathf.Sin(theta2) * domainRadius, 0);
        GL.Vertex(p1);
        GL.Vertex(p2);
    }
    GL.End();

    // --- Draw the polar point ---
    // Map the polar coordinates into screen space.
    float pointX = center.x + polarRadius * Mathf.Cos(polarAngle * Mathf.Deg2Rad) * domainRadius;
    float pointY = center.y + polarRadius * Mathf.Sin(polarAngle * Mathf.Deg2Rad) * domainRadius;
    Vector3 pointPos = new Vector3(pointX, pointY, 0);

    // Use barycentrics to compute a blended color (red, green, blue).
    Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);
    Color blended = bary.x * Color.red + bary.y * Color.green + bary.z * Color.blue;

    // Draw a filled circle at the computed polar point.
    DrawFilledCircle(pointPos, 5f, blended);

    // Draw a yellow outline around the polar point.
    GL.Begin(GL.LINE_STRIP);
    GL.Color(Color.yellow);
    int circleSegments = 20;
    for (int i = 0; i <= circleSegments; i++)
    {
        float theta = (float)i / circleSegments * 2f * Mathf.PI;
        Vector3 circlePos = new Vector3(pointPos.x + Mathf.Cos(theta) * 5f, pointPos.y + Mathf.Sin(theta) * 5f, 0);
        GL.Vertex(circlePos);
    }
    GL.End();

    GL.PopMatrix();
    DestroyImmediate(mat);
}

// Draw a filled circle using GL.TRIANGLES.
private void DrawFilledCircle(Vector3 center, float radius, Color color)
{
    int segments = 30;
    GL.Begin(GL.TRIANGLES);
    GL.Color(color);
    for (int i = 0; i < segments; i++)
    {
        float theta1 = (float)i / segments * 2f * Mathf.PI;
        float theta2 = (float)(i + 1) / segments * 2f * Mathf.PI;
        Vector3 p1 = new Vector3(center.x + Mathf.Cos(theta1) * radius, center.y + Mathf.Sin(theta1) * radius, center.z);
        Vector3 p2 = new Vector3(center.x + Mathf.Cos(theta2) * radius, center.y + Mathf.Sin(theta2) * radius, center.z);
        GL.Vertex(center);
        GL.Vertex(p1);
        GL.Vertex(p2);
    }
    GL.End();
}

// Convert polar coordinates (angle in degrees, radius [0,1]) to barycentrics.
private Vector3 PolarToBarycentrics(float angleDegrees, float radius)
{
    // Define an equilateral triangle in 2D.
    // Vertices correspond to:
    // P1: timelineValue (red), P2: oscValue1 (green), P3: oscValue2 (blue)
    Vector2 P1 = new Vector2(0, 1);
    Vector2 P2 = new Vector2(Mathf.Sqrt(3) / 2, -0.5f);
    Vector2 P3 = new Vector2(-Mathf.Sqrt(3) / 2, -0.5f);
    // The triangle's centroid is at (0,0).

    // Convert polar angle to a direction vector.
    float angleRad = angleDegrees * Mathf.Deg2Rad;
    Vector2 d = new Vector2(Mathf.Cos(angleRad), Mathf.Sin(angleRad));

    // Find the intersection of the ray (origin, direction d) with the triangle edges.
    float tMin = float.PositiveInfinity;
    float tEdge;
    if (RaySegmentIntersection(Vector2.zero, d, P1, P2, out tEdge))
        tMin = Mathf.Min(tMin, tEdge);
    if (RaySegmentIntersection(Vector2.zero, d, P2, P3, out tEdge))
        tMin = Mathf.Min(tMin, tEdge);
    if (RaySegmentIntersection(Vector2.zero, d, P3, P1, out tEdge))
        tMin = Mathf.Min(tMin, tEdge);

    // The intersection point on the triangle's edge.
    Vector2 edgePoint = d * tMin;
    // Interpolate from the center (0,0) to the edge based on the polar radius.
    Vector2 finalPoint = Vector2.Lerp(Vector2.zero, edgePoint, radius);

    // Convert the 2D point to barycentrics relative to the triangle vertices.
    Vector3 bary = ComputeBarycentrics2D(P1, P2, P3, finalPoint);
    return bary;
}

// Find the parameter 't' along a ray (origin, direction) where it intersects a segment (segA, segB).
private static bool RaySegmentIntersection(Vector2 rayOrigin, Vector2 rayDir, Vector2 segA, Vector2 segB, out float t)
{
    Vector2 v1 = rayOrigin - segA;
    Vector2 v2 = segB - segA;
    Vector2 v3 = new Vector2(-rayDir.y, rayDir.x);
    float dot = Vector2.Dot(v2, v3);
    if (Mathf.Abs(dot) < 0.0001f)
    {
        t = 0;
        return false;
    }
    float t1 = Cross(v2, v1) / dot;
    float t2 = Vector2.Dot(v1, v3) / dot;
    if (t1 >= 0 && t2 >= 0 && t2 <= 1)
    {
        t = t1;
        return true;
    }
    t = 0;
    return false;
}

// 2D cross product.
private static float Cross(Vector2 a, Vector2 b)
{
    return a.x * b.y - a.y * b.x;
}

// Compute barycentric coordinates for a 2D point P with respect to triangle vertices A, B, and C.
private static Vector3 ComputeBarycentrics2D(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
{
    float det = (B.y - C.y) * (A.x - C.x) + (C.x - B.x) * (A.y - C.y);
    float u = ((B.y - C.y) * (P.x - C.x) + (C.x - B.x) * (P.y - C.y)) / det;
    float v = ((C.y - A.y) * (P.x - C.x) + (A.x - C.x) * (P.y - C.y)) / det;
    float w = 1 - u - v;
    return new Vector3(u, v, w);
}

}

ChatGPT

Below is a modified version of your VirtualValuePolarEditor script that draws the polar circle directly in the main Inspector rather than in the Preview area. We do this by removing the OnPreviewGUI and HasPreviewGUI overrides and instead using immediate-mode drawing inside OnInspectorGUI.

Note: Using GL calls in the main inspector is somewhat unorthodox, because the Inspector is a scrolling region and not typically used for low-level graphics. For more complex or interactive 2D drawings, consider using a custom EditorWindow or the Unity UI Toolkit. But for a quick demonstration, this works fine.

---

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValuePolarEditor : Editor
{
    // Temporary polar parameters for controlling the virtual value in polar space.
    // Angle is in degrees and radius is normalized (0 at the center, 1 at the edge).
    private float polarAngle = 0f;
    private float polarRadius = 0f;

    public override void OnInspectorGUI()
    {
        // 1) Draw the default inspector (exposes timelineValue, oscValue1, oscValue2, alpha, beta, etc.).
        DrawDefaultInspector();
        EditorGUILayout.Space();

        // 2) Draw sliders for polar controls.
        EditorGUILayout.LabelField("Polar Controls", EditorStyles.boldLabel);
        polarAngle = EditorGUILayout.Slider("Polar Angle (°)", polarAngle, 0f, 360f);
        polarRadius = EditorGUILayout.Slider("Polar Radius", polarRadius, 0f, 1f);

        // 3) Convert the polar coordinates to barycentrics.
        Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);

        // 4) Display the computed barycentrics.
        EditorGUILayout.LabelField("Computed Barycentrics:",
            string.Format("u: {0:F2}, v: {1:F2}, w: {2:F2}", bary.x, bary.y, bary.z));

        // 5) Update the VirtualValue's barycentrics.
        VirtualValue vv = (VirtualValue)target;
        vv.alpha = bary.x;
        vv.beta = bary.y;

        // 6) Reserve space in the inspector to draw our circle graphic.
        //    Increase height if you want a bigger area.
        Rect drawRect = EditorGUILayout.GetControlRect(false, 200f);

        // 7) Do the custom drawing only on the Repaint event.
        if (Event.current.type == EventType.Repaint)
        {
            // Create a temporary material for our GL calls.
            Material mat = new Material(Shader.Find("Hidden/Internal-Colored"));
            mat.hideFlags = HideFlags.HideAndDontSave;

            GL.PushMatrix();
            // Set up a pixel matrix so 0,0 is at the top-left corner of drawRect,
            // and drawRect.width, drawRect.height is the bottom-right corner.
            GL.LoadPixelMatrix(0, Screen.width, Screen.height, 0);
            mat.SetPass(0);

            // We'll define our center and radius based on the reserved drawRect.
            // Because GL.LoadPixelMatrix(0, Screen.width, Screen.height, 0) uses
            // the full inspector window coordinates, we must offset by drawRect.x/y.
            Vector3 center = new Vector3(drawRect.x + drawRect.width * 0.5f,
                                         drawRect.y + drawRect.height * 0.5f, 0);
            float domainRadius = Mathf.Min(drawRect.width, drawRect.height) * 0.5f;

            // --- Draw a gray circle to represent the full "domain" of polar coords ---
            GL.Begin(GL.LINES);
            GL.Color(Color.gray);
            int segments = 60;
            for (int i = 0; i < segments; i++)
            {
                float theta1 = (float)i / segments * 2f * Mathf.PI;
                float theta2 = (float)(i + 1) / segments * 2f * Mathf.PI;
                Vector3 p1 = new Vector3(Mathf.Cos(theta1) * domainRadius, Mathf.Sin(theta1) * domainRadius, 0);
                Vector3 p2 = new Vector3(Mathf.Cos(theta2) * domainRadius, Mathf.Sin(theta2) * domainRadius, 0);

                // Offset each point by 'center'.
                p1 += center;
                p2 += center;

                GL.Vertex(p1);
                GL.Vertex(p2);
            }
            GL.End();

            // --- Draw the polar point ---
            // Map the polar coords into screen space relative to center.
            float angleRad = polarAngle * Mathf.Deg2Rad;
            float xOffset = polarRadius * Mathf.Cos(angleRad) * domainRadius;
            float yOffset = polarRadius * Mathf.Sin(angleRad) * domainRadius;
            Vector3 pointPos = center + new Vector3(xOffset, yOffset, 0);

            // Use barycentrics to compute a blended color (red, green, blue).
            Color blended = bary.x * Color.red + bary.y * Color.green + bary.z * Color.blue;

            // Draw a filled circle at 'pointPos'.
            DrawFilledCircle(pointPos, 5f, blended);

            // Draw a small yellow outline around the point.
            GL.Begin(GL.LINE_STRIP);
            GL.Color(Color.yellow);
            int circleSegments = 20;
            for (int i = 0; i <= circleSegments; i++)
            {
                float theta = (float)i / circleSegments * 2f * Mathf.PI;
                Vector3 circlePos = new Vector3(pointPos.x + Mathf.Cos(theta) * 5f,
                                                pointPos.y + Mathf.Sin(theta) * 5f, 0);
                GL.Vertex(circlePos);
            }
            GL.End();

            GL.PopMatrix();
            DestroyImmediate(mat);
        }

        // 8) Mark the object as dirty if any inspector fields changed.
        if (GUI.changed)
        {
            EditorUtility.SetDirty(target);
        }
    }

    // Draw a filled circle using GL.TRIANGLES.
    private void DrawFilledCircle(Vector3 center, float radius, Color color)
    {
        int segments = 30;
        GL.Begin(GL.TRIANGLES);
        GL.Color(color);
        for (int i = 0; i < segments; i++)
        {
            float theta1 = (float)i / segments * 2f * Mathf.PI;
            float theta2 = (float)(i + 1) / segments * 2f * Mathf.PI;
            Vector3 p1 = new Vector3(Mathf.Cos(theta1) * radius, Mathf.Sin(theta1) * radius, 0) + center;
            Vector3 p2 = new Vector3(Mathf.Cos(theta2) * radius, Mathf.Sin(theta2) * radius, 0) + center;
            GL.Vertex(center);
            GL.Vertex(p1);
            GL.Vertex(p2);
        }
        GL.End();
    }

    // Convert polar coordinates (angle in degrees, radius in [0,1]) to barycentrics.
    private Vector3 PolarToBarycentrics(float angleDegrees, float radius)
    {
        // Define an equilateral triangle in 2D (centroid at (0,0)).
        Vector2 P1 = new Vector2(0, 1);                 // timelineValue (red)
        Vector2 P2 = new Vector2(Mathf.Sqrt(3)/2, -0.5f); // oscValue1 (green)
        Vector2 P3 = new Vector2(-Mathf.Sqrt(3)/2, -0.5f); // oscValue2 (blue)

        // Convert angle to a direction vector.
        float angleRad = angleDegrees * Mathf.Deg2Rad;
        Vector2 d = new Vector2(Mathf.Cos(angleRad), Mathf.Sin(angleRad));

        // Intersect the ray from (0,0) in direction d with each triangle edge.
        float tMin = float.PositiveInfinity;
        if (RaySegmentIntersection(Vector2.zero, d, P1, P2, out float t12))
            tMin = Mathf.Min(tMin, t12);
        if (RaySegmentIntersection(Vector2.zero, d, P2, P3, out float t23))
            tMin = Mathf.Min(tMin, t23);
        if (RaySegmentIntersection(Vector2.zero, d, P3, P1, out float t31))
            tMin = Mathf.Min(tMin, t31);

        // Edge intersection point.
        Vector2 edgePoint = d * tMin;
        // Lerp from center (0,0) to edge by 'radius'.
        Vector2 finalPoint = Vector2.Lerp(Vector2.zero, edgePoint, radius);

        // Convert to barycentrics.
        return ComputeBarycentrics2D(P1, P2, P3, finalPoint);
    }

    // Ray/Segment intersection in 2D.
    private static bool RaySegmentIntersection(Vector2 rayOrigin, Vector2 rayDir, Vector2 segA, Vector2 segB, out float t)
    {
        Vector2 v1 = rayOrigin - segA;
        Vector2 v2 = segB - segA;
        Vector2 v3 = new Vector2(-rayDir.y, rayDir.x);
        float dot = Vector2.Dot(v2, v3);
        if (Mathf.Abs(dot) < 0.0001f)
        {
            t = 0;
            return false;
        }
        float t1 = Cross(v2, v1) / dot;
        float t2 = Vector2.Dot(v1, v3) / dot;
        if (t1 >= 0 && t2 >= 0 && t2 <= 1)
        {
            t = t1;
            return true;
        }
        t = 0;
        return false;
    }

    private static float Cross(Vector2 a, Vector2 b)
    {
        return a.x * b.y - a.y * b.x;
    }

    // Compute barycentric coordinates for P in triangle ABC (2D).
    private static Vector3 ComputeBarycentrics2D(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
    {
        float det = (B.y - C.y)*(A.x - C.x) + (C.x - B.x)*(A.y - C.y);
        float u = ((B.y - C.y)*(P.x - C.x) + (C.x - B.x)*(P.y - C.y)) / det;
        float v = ((C.y - A.y)*(P.x - C.x) + (A.x - C.x)*(P.y - C.y)) / det;
        float w = 1f - u - v;
        return new Vector3(u, v, w);
    }
}

Key Changes

1. Removed OnPreviewGUI and HasPreviewGUI:
   All rendering is done inside OnInspectorGUI.

2. Reserving Inspector Space:
   We call EditorGUILayout.GetControlRect(false, 200f) to create a 200 px-high region in the Inspector for drawing.

3. Drawing with GL in OnInspectorGUI:
   We do our GL drawing calls only when Event.current.type == EventType.Repaint. We set up a pixel matrix to the full Editor window space (GL.LoadPixelMatrix(0, Screen.width, Screen.height, 0)) and offset our drawing by the rectangle’s x and y coordinates.

4. Centering the Circle:
   We compute a center inside that region (drawRect.x + drawRect.width * 0.5f, etc.) so that our circle is visually centered within the allocated area.

5. Scrolling Caveat:
   If your Inspector is scrollable and the user scrolls, the drawn shapes won’t automatically track the scroll position. This is one reason many developers prefer a dedicated EditorWindow or IMGUIContainer for custom 2D visuals. But for a quick demo, this works.

With these changes, the polar circle (and the point showing your barycentric blend) will appear in the main Inspector rather than in the Preview pane.

You

but this ignores completely the existing UI layout and draw the circle in a random location. I want a circle drawn properly after the other UI elements

ChatGPT

Below is a revised version of your custom editor that draws both a polar domain (a circle) and an equilateral triangle within the main Inspector layout. In this version we reserve a specific control area (using EditorGUILayout.GetControlRect) and then split it horizontally into two groups—one for the polar circle and one for the triangle. By using GUI.BeginGroup we ensure our drawings respect the layout instead of appearing in an arbitrary location.

Place the script in your Editor folder (for example, “Editor/VirtualValuePolarEditor.cs”):

---

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValuePolarEditor : Editor
{
    // Temporary polar parameters for controlling the virtual value in polar space.
    // Angle is in degrees and radius is normalized (0 at the center, 1 at the edge).
    private float polarAngle = 0f;
    private float polarRadius = 0f;

    public override void OnInspectorGUI()
    {
        // 1) Draw the default inspector (fields, etc.)
        DrawDefaultInspector();
        EditorGUILayout.Space();

        // 2) Draw polar controls
        EditorGUILayout.LabelField("Polar Controls", EditorStyles.boldLabel);
        polarAngle = EditorGUILayout.Slider("Polar Angle (°)", polarAngle, 0f, 360f);
        polarRadius = EditorGUILayout.Slider("Polar Radius", polarRadius, 0f, 1f);

        // 3) Convert the polar coordinates to barycentrics.
        Vector3 bary = PolarToBarycentrics(polarAngle, polarRadius);

        // 4) Display the computed barycentrics.
        EditorGUILayout.LabelField("Computed Barycentrics:",
            string.Format("u: {0:F2}, v: {1:F2}, w: {2:F2}", bary.x, bary.y, bary.z));

        // 5) Update the VirtualValue's barycentrics.
        VirtualValue vv = (VirtualValue)target;
        vv.alpha = bary.x;
        vv.beta = bary.y;

        EditorGUILayout.Space();
        EditorGUILayout.LabelField("Visualizations", EditorStyles.boldLabel);

        // 6) Reserve a rectangular area to draw our two shapes (circle and triangle)
        Rect overallRect = EditorGUILayout.GetControlRect(false, 200f);
        float halfWidth = overallRect.width * 0.5f;
        Rect circleRect = new Rect(overallRect.x, overallRect.y, halfWidth, overallRect.height);
        Rect triangleRect = new Rect(overallRect.x + halfWidth, overallRect.y, halfWidth, overallRect.height);

        // 7) Draw the polar circle in its designated area.
        GUI.BeginGroup(circleRect);
        {
            // Use Handles to draw within the group.
            Handles.BeginGUI();

            // Define the circle's local center and domain radius.
            Vector2 circleCenter = new Vector2(circleRect.width * 0.5f, circleRect.height * 0.5f);
            float domainRadius = Mathf.Min(circleRect.width, circleRect.height) * 0.5f - 5f;

            // Draw the polar domain as a gray wire disc.
            Handles.color = Color.gray;
            Handles.DrawWireDisc(circleCenter, Vector3.forward, domainRadius);

            // Compute the polar point relative to the circle.
            float angleRad = polarAngle * Mathf.Deg2Rad;
            float xOffset = polarRadius * Mathf.Cos(angleRad) * domainRadius;
            float yOffset = polarRadius * Mathf.Sin(angleRad) * domainRadius;
            Vector2 polarPoint = circleCenter + new Vector2(xOffset, yOffset);

            // Compute a blended color using the barycentrics.
            Color blended = bary.x * Color.red + bary.y * Color.green + bary.z * Color.blue;

            // Draw the polar point as a small filled disc.
            Handles.color = blended;
            Handles.DrawSolidDisc(polarPoint, Vector3.forward, 5f);
            // Draw a yellow outline around the point.
            Handles.color = Color.yellow;
            Handles.DrawWireDisc(polarPoint, Vector3.forward, 5f);

            Handles.EndGUI();
        }
        GUI.EndGroup();

        // 8) Draw the triangle in its designated area.
        GUI.BeginGroup(triangleRect);
        {
            Handles.BeginGUI();

            // Define an equilateral triangle.
            Vector2 triCenter = new Vector2(triangleRect.width * 0.5f, triangleRect.height * 0.5f);
            // Choose a scale that fits nicely in the rect.
            float triScale = Mathf.Min(triangleRect.width, triangleRect.height) * 0.4f;
            // Vertices of the triangle (using an equilateral triangle)
            Vector2 v1 = triCenter + new Vector2(0, triScale);                          // Top (red)
            Vector2 v2 = triCenter + new Vector2(triScale * Mathf.Sqrt(3) / 2f, -triScale * 0.5f); // Bottom right (green)
            Vector2 v3 = triCenter + new Vector2(-triScale * Mathf.Sqrt(3) / 2f, -triScale * 0.5f); // Bottom left (blue)

            // Draw the triangle edges with vertex colors.
            Handles.color = Color.red;
            Handles.DrawLine(v1, v2);
            Handles.color = Color.green;
            Handles.DrawLine(v2, v3);
            Handles.color = Color.blue;
            Handles.DrawLine(v3, v1);

            // Compute the point inside the triangle using barycentrics.
            Vector2 triPoint = bary.x * v1 + bary.y * v2 + bary.z * v3;
            Color blendedTri = bary.x * Color.red + bary.y * Color.green + bary.z * Color.blue;
            // Draw the polar point (converted via barycentrics) in the triangle.
            Handles.color = blendedTri;
            Handles.DrawSolidDisc(triPoint, Vector3.forward, 5f);
            Handles.color = Color.yellow;
            Handles.DrawWireDisc(triPoint, Vector3.forward, 5f);

            Handles.EndGUI();
        }
        GUI.EndGroup();

        if (GUI.changed)
        {
            EditorUtility.SetDirty(target);
        }
    }

    // Convert polar coordinates (angle in degrees, radius in [0,1]) to barycentrics.
    private Vector3 PolarToBarycentrics(float angleDegrees, float radius)
    {
        // Define an equilateral triangle in 2D (centroid at (0,0)).
        // Vertices correspond to:
        //   P1: timelineValue (red), P2: oscValue1 (green), P3: oscValue2 (blue)
        Vector2 P1 = new Vector2(0, 1);
        Vector2 P2 = new Vector2(Mathf.Sqrt(3) / 2, -0.5f);
        Vector2 P3 = new Vector2(-Mathf.Sqrt(3) / 2, -0.5f);

        // Convert polar angle to a direction vector.
        float angleRad = angleDegrees * Mathf.Deg2Rad;
        Vector2 d = new Vector2(Mathf.Cos(angleRad), Mathf.Sin(angleRad));

        // Find the intersection of the ray (origin, direction d) with each triangle edge.
        float tMin = float.PositiveInfinity;
        if (RaySegmentIntersection(Vector2.zero, d, P1, P2, out float t12))
            tMin = Mathf.Min(tMin, t12);
        if (RaySegmentIntersection(Vector2.zero, d, P2, P3, out float t23))
            tMin = Mathf.Min(tMin, t23);
        if (RaySegmentIntersection(Vector2.zero, d, P3, P1, out float t31))
            tMin = Mathf.Min(tMin, t31);

        // The intersection point on the triangle's edge.
        Vector2 edgePoint = d * tMin;
        // Interpolate from the center (0,0) to the edge based on the polar radius.
        Vector2 finalPoint = Vector2.Lerp(Vector2.zero, edgePoint, radius);

        // Convert the 2D point to barycentrics relative to the triangle vertices.
        return ComputeBarycentrics2D(P1, P2, P3, finalPoint);
    }

    // Ray/segment intersection in 2D.
    private static bool RaySegmentIntersection(Vector2 rayOrigin, Vector2 rayDir, Vector2 segA, Vector2 segB, out float t)
    {
        Vector2 v1 = rayOrigin - segA;
        Vector2 v2 = segB - segA;
        Vector2 v3 = new Vector2(-rayDir.y, rayDir.x);
        float dot = Vector2.Dot(v2, v3);
        if (Mathf.Abs(dot) < 0.0001f)
        {
            t = 0;
            return false;
        }
        float t1 = Cross(v2, v1) / dot;
        float t2 = Vector2.Dot(v1, v3) / dot;
        if (t1 >= 0 && t2 >= 0 && t2 <= 1)
        {
            t = t1;
            return true;
        }
        t = 0;
        return false;
    }

    private static float Cross(Vector2 a, Vector2 b)
    {
        return a.x * b.y - a.y * b.x;
    }

    // Compute barycentrics for point P relative to triangle ABC (2D).
    private static Vector3 ComputeBarycentrics2D(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
    {
        float det = (B.y - C.y) * (A.x - C.x) + (C.x - B.x) * (A.y - C.y);
        float u = ((B.y - C.y) * (P.x - C.x) + (C.x - B.x) * (P.y - C.y)) / det;
        float v = ((C.y - A.y) * (P.x - C.x) + (A.x - C.x) * (P.y - C.y)) / det;
        float w = 1f - u - v;
        return new Vector3(u, v, w);
    }
}

---

How This Works

1. Reserving Layout Space:
   We reserve a 200-pixel-high control area using EditorGUILayout.GetControlRect. Then we split that area horizontally into two groups: one for the polar circle and one for the triangle.

2. Drawing Inside Groups:
   Using GUI.BeginGroup on each sub-rectangle makes the drawing coordinate system local to that area—ensuring your shapes appear right after the other UI elements and not in a random position.

3. Drawing the Circle (Polar Domain):
   In the left group we use Handles to draw a gray wire disc representing the full polar domain. The polar point (computed from polarAngle and polarRadius) is drawn as a small filled disc with its color blended from the barycentrics, then outlined in yellow.

4. Drawing the Triangle:
   In the right group we define an equilateral triangle (with vertices colored red, green, and blue). The barycentric (blended) point is then computed as a weighted sum of the vertices and drawn in the triangle.

This revised script integrates your drawing into the Inspector’s UI layout so that the visual elements appear properly after your other UI controls.

You

Ok this is great. I now want to express the angle as 1,2,3, not 0-360 and interpolate through these.

I also want 3 helpful buttins, that when pressed they automatically set the correct value to land on a triangle’s corner

ChatGPT

Below is an updated version of the custom editor. In this version the polar “angle” is now expressed as a continuous value between 1 and 3. Internally, we map:

• 1 → 90° (triangle corner 1),
• 2 → 210° (triangle corner 2),
• 3 → 330° (triangle corner 3).

Values in between are interpolated. Also, three buttons let you jump directly to the three triangle corners (and we set the radius to 1 so the point lands exactly on the vertex).

Place this script in your Editor folder (e.g. “Editor/VirtualValuePolarEditor.cs”):

---

using UnityEngine;
using UnityEditor;

[CustomEditor(typeof(VirtualValue))]
public class VirtualValuePolarEditor : Editor
{
    // Temporary parameters for controlling the virtual value in polar space.
    // "polarCorner" is now expressed as a continuous value from 1 to 3.
    // A value of 1 means corner 1, 2 means corner 2, 3 means corner 3,
    // with interpolation in between.
    private float polarCorner = 1f;
    // Radius remains [0,1]: 0 at center, 1 at the edge.
    private float polarRadius = 0f;

    public override void OnInspectorGUI()
    {
        // 1) Draw default inspector (exposes timelineValue, oscValue1, oscValue2, etc.)
        DrawDefaultInspector();
        EditorGUILayout.Space();

        // 2) Draw polar controls.
        EditorGUILayout.LabelField("Polar Controls (Expressed as 1,2,3)", EditorStyles.boldLabel);
        // Slider for the "corner" parameter. It ranges from 1 to 3.
        polarCorner = EditorGUILayout.Slider("Corner", polarCorner, 1f, 3f);
        // Slider for the polar radius.
        polarRadius = EditorGUILayout.Slider("Polar Radius", polarRadius, 0f, 1f);

        // 3) Provide three buttons for quickly jumping to a triangle's corner.
        EditorGUILayout.BeginHorizontal();
        if (GUILayout.Button("Corner 1"))
        {
            polarCorner = 1f;
            polarRadius = 1f; // exactly on the vertex
        }
        if (GUILayout.Button("Corner 2"))
        {
            polarCorner = 2f;
            polarRadius = 1f;
        }
        if (GUILayout.Button("Corner 3"))
        {
            polarCorner = 3f;
            polarRadius = 1f;
        }
        EditorGUILayout.EndHorizontal();

        // 4) Convert the discrete "corner" to an angle in degrees.
        float angleDegrees = DiscreteCornerToAngle(polarCorner);

        // 5) Convert polar (angle in degrees, radius) to barycentrics.
        Vector3 bary = PolarToBarycentrics(angleDegrees, polarRadius);

        // 6) Display the computed barycentrics.
        EditorGUILayout.LabelField("Computed Barycentrics:",
            string.Format("u: {0:F2}, v: {1:F2}, w: {2:F2}", bary.x, bary.y, bary.z));

        // 7) Update the VirtualValue's barycentrics.
        VirtualValue vv = (VirtualValue)target;
        vv.alpha = bary.x;
        vv.beta = bary.y;

        EditorGUILayout.Space();
        EditorGUILayout.LabelField("Visualizations", EditorStyles.boldLabel);

        // 8) Reserve a rectangular area for drawing both the polar circle and the triangle.
        Rect overallRect = EditorGUILayout.GetControlRect(false, 200f);
        float halfWidth = overallRect.width * 0.5f;
        Rect circleRect = new Rect(overallRect.x, overallRect.y, halfWidth, overallRect.height);
        Rect triangleRect = new Rect(overallRect.x + halfWidth, overallRect.y, halfWidth, overallRect.height);

        // 9) Draw the polar circle in its designated area.
        GUI.BeginGroup(circleRect);
        {
            Handles.BeginGUI();
            // Define the local center and radius of the polar domain.
            Vector2 circleCenter = new Vector2(circleRect.width * 0.5f, circleRect.height * 0.5f);
            float domainRadius = Mathf.Min(circleRect.width, circleRect.height) * 0.5f - 5f;

            // Draw the polar domain as a gray wire disc.
            Handles.color = Color.gray;
            Handles.DrawWireDisc(circleCenter, Vector3.forward, domainRadius);

            // Compute the polar point using our mapped angle.
            float angleRad = angleDegrees * Mathf.Deg2Rad;
            float xOffset = polarRadius * Mathf.Cos(angleRad) * domainRadius;
            float yOffset = polarRadius * Mathf.Sin(angleRad) * domainRadius;
            Vector2 polarPoint = circleCenter + new Vector2(xOffset, yOffset);

            // Compute a blended color based on barycentrics.
            Color blended = bary.x * Color.red + bary.y * Color.green + bary.z * Color.blue;

            // Draw the polar point.
            Handles.color = blended;
            Handles.DrawSolidDisc(polarPoint, Vector3.forward, 5f);
            Handles.color = Color.yellow;
            Handles.DrawWireDisc(polarPoint, Vector3.forward, 5f);

            Handles.EndGUI();
        }
        GUI.EndGroup();

        // 10) Draw the triangle visualization.
        GUI.BeginGroup(triangleRect);
        {
            Handles.BeginGUI();
            // Define an equilateral triangle.
            Vector2 triCenter = new Vector2(triangleRect.width * 0.5f, triangleRect.height * 0.5f);
            float triScale = Mathf.Min(triangleRect.width, triangleRect.height) * 0.4f;
            // Use the same vertices as our polar-to-barycentrics mapping.
            Vector2 v1 = triCenter + new Vector2(0, triScale);                           // Corner 1 (red)
            Vector2 v2 = triCenter + new Vector2(-triScale * Mathf.Sqrt(3)/2f, -triScale * 0.5f); // Corner 2 (blue)
            Vector2 v3 = triCenter + new Vector2(triScale * Mathf.Sqrt(3)/2f, -triScale * 0.5f);  // Corner 3 (green)

            // Draw triangle edges.
            Handles.color = Color.red;
            Handles.DrawLine(v1, v2);
            Handles.color = Color.blue;
            Handles.DrawLine(v2, v3);
            Handles.color = Color.green;
            Handles.DrawLine(v3, v1);

            // Compute the point inside the triangle using barycentrics.
            Vector2 triPoint = bary.x * v1 + bary.y * v2 + bary.z * v3;
            Color blendedTri = bary.x * Color.red + bary.y * Color.blue + bary.z * Color.green;
            Handles.color = blendedTri;
            Handles.DrawSolidDisc(triPoint, Vector3.forward, 5f);
            Handles.color = Color.yellow;
            Handles.DrawWireDisc(triPoint, Vector3.forward, 5f);

            Handles.EndGUI();
        }
        GUI.EndGroup();

        if (GUI.changed)
        {
            EditorUtility.SetDirty(target);
        }
    }

    /// <summary>
    /// Maps a value in [1,3] to an angle in degrees corresponding to the triangle's corners.
    /// Corner 1 = 90°, Corner 2 = 210°, Corner 3 = 330°.
    /// Values in between are linearly interpolated along the shortest arc.
    /// </summary>
    private float DiscreteCornerToAngle(float t)
    {
        if (t <= 2f)
            return Mathf.Lerp(90f, 210f, t - 1f);
        else
            return Mathf.Lerp(210f, 330f, t - 2f);
    }

    // Convert polar coordinates (angle in degrees, radius in [0,1]) to barycentrics.
    private Vector3 PolarToBarycentrics(float angleDegrees, float radius)
    {
        // Define an equilateral triangle in 2D.
        // Vertices correspond to:
        //   P1: timelineValue (red) at (0,1) → 90°
        //   P2: oscValue1 (green) at (√3/2,-0.5) → 330°
        //   P3: oscValue2 (blue) at (-√3/2,-0.5) → 210°
        Vector2 P1 = new Vector2(0, 1);
        Vector2 P2 = new Vector2(Mathf.Sqrt(3) / 2, -0.5f);
        Vector2 P3 = new Vector2(-Mathf.Sqrt(3) / 2, -0.5f);

        // Convert the angle to a direction vector.
        float angleRad = angleDegrees * Mathf.Deg2Rad;
        Vector2 d = new Vector2(Mathf.Cos(angleRad), Mathf.Sin(angleRad));

        // Find intersection of ray (origin,d) with each triangle edge.
        float tMin = float.PositiveInfinity;
        if (RaySegmentIntersection(Vector2.zero, d, P1, P2, out float t12))
            tMin = Mathf.Min(tMin, t12);
        if (RaySegmentIntersection(Vector2.zero, d, P2, P3, out float t23))
            tMin = Mathf.Min(tMin, t23);
        if (RaySegmentIntersection(Vector2.zero, d, P3, P1, out float t31))
            tMin = Mathf.Min(tMin, t31);

        // Intersection point on the triangle's edge.
        Vector2 edgePoint = d * tMin;
        // Lerp from center (0,0) to the edge based on radius.
        Vector2 finalPoint = Vector2.Lerp(Vector2.zero, edgePoint, radius);

        return ComputeBarycentrics2D(P1, P2, P3, finalPoint);
    }

    // Computes the intersection of a ray and a segment in 2D.
    private static bool RaySegmentIntersection(Vector2 rayOrigin, Vector2 rayDir, Vector2 segA, Vector2 segB, out float t)
    {
        Vector2 v1 = rayOrigin - segA;
        Vector2 v2 = segB - segA;
        Vector2 v3 = new Vector2(-rayDir.y, rayDir.x);
        float dot = Vector2.Dot(v2, v3);
        if (Mathf.Abs(dot) < 0.0001f)
        {
            t = 0;
            return false;
        }
        float t1 = Cross(v2, v1) / dot;
        float t2 = Vector2.Dot(v1, v3) / dot;
        if (t1 >= 0 && t2 >= 0 && t2 <= 1)
        {
            t = t1;
            return true;
        }
        t = 0;
        return false;
    }

    private static float Cross(Vector2 a, Vector2 b)
    {
        return a.x * b.y - a.y * b.x;
    }

    // Compute barycentrics for point P with respect to triangle ABC (2D).
    private static Vector3 ComputeBarycentrics2D(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
    {
        float det = (B.y - C.y) * (A.x - C.x) + (C.x - B.x) * (A.y - C.y);
        float u = ((B.y - C.y) * (P.x - C.x) + (C.x - B.x) * (P.y - C.y)) / det;
        float v = ((C.y - A.y) * (P.x - C.x) + (A.x - C.x) * (P.y - C.y)) / det;
        float w = 1f - u - v;
        return new Vector3(u, v, w);
    }
}

---

How It Works

1. Slider Changes:
   The “Corner” slider now ranges from 1 to 3. We use the helper method DiscreteCornerToAngle to convert this value to an angle in degrees (with 1 mapping to 90°, 2 to 210°, and 3 to 330°). In-between values interpolate linearly.

2. Helpful Buttons:
   Three buttons labeled “Corner 1”, “Corner 2”, and “Corner 3” are drawn. When pressed they set the slider value (polarCorner) to 1, 2, or 3, and set the radius to 1 so that the polar point lands exactly on the corresponding triangle vertex.

3. Conversion to Barycentrics & Drawing:
   The computed angle (in degrees) and the radius are passed into PolarToBarycentrics which calculates the barycentrics. These values update the VirtualValue’s internal weights. The polar domain (a circle) and the triangle (with the blended point) are drawn in separate groups within the Inspector layout, ensuring they appear in the correct place.

This approach now lets you work with an intuitive “corner” parameter (1, 2, or 3) and quickly jump to each triangle vertex via buttons, while still allowing smooth interpolation between them.