forked from BilalY/Rasagar
201 lines
8.3 KiB
C#
201 lines
8.3 KiB
C#
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using UnityEngine;
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namespace Cinemachine.Utility
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{
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/// <summary>
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/// A collection of utilities relating to Bezier splines
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/// </summary>
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public static class SplineHelpers
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{
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/// <summary>Compute the value of a 4-point 3-dimensional bezier spline</summary>
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/// <param name="t">How far along the spline (0...1)</param>
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/// <param name="p0">First point</param>
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/// <param name="p1">First tangent</param>
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/// <param name="p2">Second point</param>
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/// <param name="p3">Second tangent</param>
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/// <returns>The spline value at t</returns>
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public static Vector3 Bezier3(
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float t, Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3)
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{
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t = Mathf.Clamp01(t);
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float d = 1f - t;
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return d * d * d * p0 + 3f * d * d * t * p1
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+ 3f * d * t * t * p2 + t * t * t * p3;
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}
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/// <summary>Compute the tangent of a 4-point 3-dimensional bezier spline</summary>
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/// <param name="t">How far along the spline (0...1)</param>
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/// <param name="p0">First point</param>
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/// <param name="p1">First tangent</param>
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/// <param name="p2">Second point</param>
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/// <param name="p3">Second tangent</param>
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/// <returns>The spline tangent at t</returns>
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public static Vector3 BezierTangent3(
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float t, Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3)
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{
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t = Mathf.Clamp01(t);
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return (-3f * p0 + 9f * p1 - 9f * p2 + 3f * p3) * (t * t)
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+ (6f * p0 - 12f * p1 + 6f * p2) * t
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- 3f * p0 + 3f * p1;
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}
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/// <summary>Compute the weights for the tangent of a 4-point 3-dimensional bezier spline</summary>
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/// <param name="p0">First point</param>
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/// <param name="p1">First tangent</param>
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/// <param name="p2">Second point</param>
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/// <param name="p3">Second tangent</param>
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/// <param name="w0">First output weight</param>
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/// <param name="w1">Second output weight</param>
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/// <param name="w2">Third output weight</param>
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public static void BezierTangentWeights3(
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Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3,
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out Vector3 w0, out Vector3 w1, out Vector3 w2)
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{
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w0 = -3f * p0 + 9f * p1 - 9f * p2 + 3f * p3;
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w1 = 6f * p0 - 12f * p1 + 6f * p2;
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w2 = -3f * p0 + 3f * p1;
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}
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/// <summary>Compute the value of a 4-point 1-dimensional bezier spline</summary>
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/// <param name="t">How far along the spline (0...1)</param>
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/// <param name="p0">First point</param>
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/// <param name="p1">First tangent</param>
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/// <param name="p2">Second point</param>
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/// <param name="p3">Second tangent</param>
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/// <returns>The spline value at t</returns>
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public static float Bezier1(float t, float p0, float p1, float p2, float p3)
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{
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t = Mathf.Clamp01(t);
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float d = 1f - t;
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return d * d * d * p0 + 3f * d * d * t * p1
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+ 3f * d * t * t * p2 + t * t * t * p3;
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}
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/// <summary>Compute the tangent of a 4-point 1-dimensional bezier spline</summary>
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/// <param name="t">How far along the spline (0...1)</param>
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/// <param name="p0">First point</param>
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/// <param name="p1">First tangent</param>
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/// <param name="p2">Second point</param>
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/// <param name="p3">Second tangent</param>
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/// <returns>The spline tangent at t</returns>
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public static float BezierTangent1(
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float t, float p0, float p1, float p2, float p3)
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{
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t = Mathf.Clamp01(t);
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return (-3f * p0 + 9f * p1 - 9f * p2 + 3f * p3) * t * t
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+ (6f * p0 - 12f * p1 + 6f * p2) * t
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- 3f * p0 + 3f * p1;
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}
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/// <summary>
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/// Use the Thomas algorithm to compute smooth tangent values for a spline.
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/// Resultant tangents guarantee second-order smoothness of the curve.
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/// </summary>
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/// <param name="knot">The knots defining the curve</param>
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/// <param name="ctrl1">Output buffer for the first control points (1 per knot)</param>
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/// <param name="ctrl2">Output buffer for the second control points (1 per knot)</param>
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public static void ComputeSmoothControlPoints(
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ref Vector4[] knot, ref Vector4[] ctrl1, ref Vector4[] ctrl2)
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{
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int numPoints = knot.Length;
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if (numPoints <= 2)
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{
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if (numPoints == 2)
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{
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ctrl1[0] = Vector4.Lerp(knot[0], knot[1], 0.33333f);
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ctrl2[0] = Vector4.Lerp(knot[0], knot[1], 0.66666f);
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}
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else if (numPoints == 1)
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ctrl1[0] = ctrl2[0] = knot[0];
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return;
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}
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var a = new float[numPoints];
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var b = new float[numPoints];
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var c = new float[numPoints];
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var r = new float[numPoints];
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for (int axis = 0; axis < 4; ++axis)
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{
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int n = numPoints - 1;
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// Linear into the first segment
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a[0] = 0;
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b[0] = 2;
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c[0] = 1;
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r[0] = knot[0][axis] + 2 * knot[1][axis];
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// Internal segments
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for (int i = 1; i < n - 1; ++i)
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{
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a[i] = 1;
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b[i] = 4;
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c[i] = 1;
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r[i] = 4 * knot[i][axis] + 2 * knot[i+1][axis];
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}
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// Linear out of the last segment
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a[n - 1] = 2;
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b[n - 1] = 7;
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c[n - 1] = 0;
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r[n - 1] = 8 * knot[n - 1][axis] + knot[n][axis];
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// Solve with Thomas algorithm
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for (int i = 1; i < n; ++i)
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{
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float m = a[i] / b[i-1];
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b[i] = b[i] - m * c[i-1];
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r[i] = r[i] - m * r[i-1];
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}
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// Compute ctrl1
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ctrl1[n-1][axis] = r[n-1] / b[n-1];
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for (int i = n - 2; i >= 0; --i)
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ctrl1[i][axis] = (r[i] - c[i] * ctrl1[i + 1][axis]) / b[i];
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// Compute ctrl2 from ctrl1
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for (int i = 0; i < n; i++)
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ctrl2[i][axis] = 2 * knot[i + 1][axis] - ctrl1[i + 1][axis];
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ctrl2[n - 1][axis] = 0.5f * (knot[n][axis] + ctrl1[n - 1][axis]);
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}
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}
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/// <summary>
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/// Use the Thomas algorithm to compute smooth tangent values for a spline.
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/// This method will assume that the spline is looped (i.e. that the last knot is followed by the first).
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/// Resultant tangents guarantee second-order smoothness of the curve.
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/// </summary>
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/// <param name="knot">The knots defining the curve</param>
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/// <param name="ctrl1">Output buffer for the first control points (1 per knot)</param>
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/// <param name="ctrl2">Output buffer for the second control points (1 per knot)</param>
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public static void ComputeSmoothControlPointsLooped(
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ref Vector4[] knot, ref Vector4[] ctrl1, ref Vector4[] ctrl2)
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{
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int numPoints = knot.Length;
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if (numPoints < 2)
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{
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if (numPoints == 1)
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ctrl1[0] = ctrl2[0] = knot[0];
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return;
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}
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int margin = Mathf.Min(4, numPoints-1);
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Vector4[] knotLooped = new Vector4[numPoints + 2 * margin];
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Vector4[] ctrl1Looped = new Vector4[numPoints + 2 * margin];
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Vector4[] ctrl2Looped = new Vector4[numPoints + 2 * margin];
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for (int i = 0; i < margin; ++i)
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{
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knotLooped[i] = knot[numPoints-(margin-i)];
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knotLooped[numPoints+margin+i] = knot[i];
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}
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for (int i = 0; i < numPoints; ++i)
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knotLooped[i + margin] = knot[i];
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ComputeSmoothControlPoints(ref knotLooped, ref ctrl1Looped, ref ctrl2Looped);
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for (int i = 0; i < numPoints; ++i)
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{
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ctrl1[i] = ctrl1Looped[i + margin];
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ctrl2[i] = ctrl2Looped[i + margin];
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}
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}
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}
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}
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