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944 lines
36 KiB
C#
944 lines
36 KiB
C#
3 years ago
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/// Original version from ProBuilder 4.0.
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/// Certains methods have been stripped out due to dependencies.
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using System;
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using System.Collections.Generic;
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namespace UnityEngine.Polybrush
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{
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/// <summary>
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/// A collection of math functions that are useful when working with 3d meshes.
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/// </summary>
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public static class Math
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{
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/// <summary>
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/// Pi / 2.
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/// </summary>
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public const float phi = 1.618033988749895f;
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/// <summary>
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/// ProBuilder epsilon constant.
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/// </summary>
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const float k_FltEpsilon = float.Epsilon;
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/// <summary>
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/// Epsilon to use when comparing vertex positions for equality.
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/// </summary>
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const float k_FltCompareEpsilon = .0001f;
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/// <summary>
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/// The minimum distance a handle must move on an axis before considering that axis as engaged.
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/// </summary>
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internal const float handleEpsilon = .0001f;
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/// <summary>
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/// Get a point on the circumference of a circle.
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/// </summary>
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/// <param name="radius">The radius of the circle.</param>
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/// <param name="angleInDegrees">Where along the circle should the point be projected. Angle is in degrees.</param>
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/// <param name="origin"></param>
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/// <returns></returns>
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internal static Vector2 PointInCircumference(float radius, float angleInDegrees, Vector2 origin)
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{
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// Convert from degrees to radians via multiplication by PI/180
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float x = (float)(radius * Mathf.Cos(Mathf.Deg2Rad * angleInDegrees)) + origin.x;
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float y = (float)(radius * Mathf.Sin(Mathf.Deg2Rad * angleInDegrees)) + origin.y;
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return new Vector2(x, y);
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}
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/// <summary>
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/// Provided a radius, latitudinal and longitudinal angle, return a position.
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/// </summary>
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/// <param name="radius"></param>
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/// <param name="latitudeAngle"></param>
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/// <param name="longitudeAngle"></param>
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/// <returns></returns>
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internal static Vector3 PointInSphere(float radius, float latitudeAngle, float longitudeAngle)
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{
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float x = (radius * Mathf.Cos(Mathf.Deg2Rad * latitudeAngle) * Mathf.Sin(Mathf.Deg2Rad * longitudeAngle));
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float y = (radius * Mathf.Sin(Mathf.Deg2Rad * latitudeAngle) * Mathf.Sin(Mathf.Deg2Rad * longitudeAngle));
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float z = (radius * Mathf.Cos(Mathf.Deg2Rad * longitudeAngle));
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return new Vector3(x, y, z);
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}
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/// <summary>
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/// Find the signed angle from direction a to direction b.
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/// </summary>
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/// <param name="a">The direction from which to rotate.</param>
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/// <param name="b">The direction to rotate towards.</param>
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/// <returns>A signed angle in degrees from direction a to direction b.</returns>
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internal static float SignedAngle(Vector2 a, Vector2 b)
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{
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float t = Vector2.Angle(a, b);
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if (b.x - a.x < 0)
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t = 360f - t;
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return t;
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}
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/// <summary>
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/// Squared distance between two points. This is the same as `(b - a).sqrMagnitude`.
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/// </summary>
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/// <param name="a">First point.</param>
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/// <param name="b">Second point.</param>
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/// <returns></returns>
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public static float SqrDistance(Vector3 a, Vector3 b)
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{
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float dx = b.x - a.x,
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dy = b.y - a.y,
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dz = b.z - a.z;
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return dx * dx + dy * dy + dz * dz;
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}
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/// <summary>
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/// Get the area of a triangle.
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/// </summary>
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/// <remarks>http://www.iquilezles.org/blog/?p=1579</remarks>
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/// <param name="x">First vertex position of the triangle.</param>
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/// <param name="y">Second vertex position of the triangle.</param>
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/// <param name="z">Third vertex position of the triangle.</param>
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/// <returns>The area of the triangle.</returns>
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public static float TriangleArea(Vector3 x, Vector3 y, Vector3 z)
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{
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float a = SqrDistance(x, y),
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b = SqrDistance(y, z),
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c = SqrDistance(z, x);
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return Mathf.Sqrt((2f * a * b + 2f * b * c + 2f * c * a - a * a - b * b - c * c) / 16f);
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}
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/// <summary>
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/// Returns the Area of a polygon.
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/// </summary>
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/// <param name="vertices"></param>
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/// <param name="indexes"></param>
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/// <returns></returns>
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internal static float PolygonArea(Vector3[] vertices, int[] indexes)
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{
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float area = 0f;
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for (int i = 0; i < indexes.Length; i += 3)
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area += TriangleArea(vertices[indexes[i]], vertices[indexes[i + 1]], vertices[indexes[i + 2]]);
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return area;
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}
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/// <summary>
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/// Returns a new point by rotating the Vector2 around an origin point.
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/// </summary>
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/// <param name="v">Vector2 original point.</param>
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/// <param name="origin">The pivot to rotate around.</param>
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/// <param name="theta">How far to rotate in degrees.</param>
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/// <returns></returns>
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internal static Vector2 RotateAroundPoint(this Vector2 v, Vector2 origin, float theta)
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{
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float cx = origin.x, cy = origin.y; // origin
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float px = v.x, py = v.y; // point
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float s = Mathf.Sin(theta * Mathf.Deg2Rad);
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float c = Mathf.Cos(theta * Mathf.Deg2Rad);
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// translate point back to origin:
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px -= cx;
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py -= cy;
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// rotate point
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float xnew = px * c + py * s;
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float ynew = -px * s + py * c;
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// translate point back:
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px = xnew + cx;
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py = ynew + cy;
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return new Vector2(px, py);
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}
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/// <summary>
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/// Scales a Vector2 using origin as the pivot point.
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/// </summary>
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/// <param name="v"></param>
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/// <param name="origin"></param>
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/// <param name="scale"></param>
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/// <returns></returns>
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public static Vector2 ScaleAroundPoint(this Vector2 v, Vector2 origin, Vector2 scale)
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{
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Vector2 tp = v - origin;
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tp = Vector2.Scale(tp, scale);
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tp += origin;
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return tp;
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}
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/// <summary>
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/// Reflects a point across a line segment.
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/// </summary>
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/// <param name="point">The point to reflect.</param>
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/// <param name="lineStart">First point of the line segment.</param>
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/// <param name="lineEnd">Second point of the line segment.</param>
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/// <returns>The reflected point.</returns>
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public static Vector2 ReflectPoint(Vector2 point, Vector2 lineStart, Vector2 lineEnd)
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{
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Vector2 line = lineEnd - lineStart;
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Vector2 perp = new Vector2(-line.y, line.x); // skip normalize
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float dist = Mathf.Sin(Vector2.Angle(line, point - lineStart) * Mathf.Deg2Rad) * Vector2.Distance(point, lineStart);
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return point + perp * (dist * 2f) * (Vector2.Dot(point - lineStart, perp) > 0 ? -1f : 1f);
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}
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internal static float SqrDistanceRayPoint(Ray ray, Vector3 point)
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{
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return Vector3.Cross(ray.direction, point - ray.origin).sqrMagnitude;
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}
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/// <summary>
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/// Get the distance between a point and a finite line segment.
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/// </summary>
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/// <remarks>http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment</remarks>
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/// <param name="point">The point.</param>
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/// <param name="lineStart">Line start.</param>
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/// <param name="lineEnd">Line end.</param>
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/// <returns>The distance from point to the nearest point on a line segment.</returns>
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public static float DistancePointLineSegment(Vector2 point, Vector2 lineStart, Vector2 lineEnd)
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{
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// Return minimum distance between line segment vw and point p
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float l2 = ((lineStart.x - lineEnd.x) * (lineStart.x - lineEnd.x)) + ((lineStart.y - lineEnd.y) * (lineStart.y - lineEnd.y)); // i.e. |w-v|^2 - avoid a sqrt
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if (l2 == 0.0f) return Vector2.Distance(point, lineStart); // v == w case
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// Consider the line extending the segment, parameterized as v + t (w - v).
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// We find projection of point p onto the line.
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// It falls where t = [(p-v) . (w-v)] / |w-v|^2
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float t = Vector2.Dot(point - lineStart, lineEnd - lineStart) / l2;
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if (t < 0.0)
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return Vector2.Distance(point, lineStart); // Beyond the 'v' end of the segment
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else if (t > 1.0)
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return Vector2.Distance(point, lineEnd); // Beyond the 'w' end of the segment
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Vector2 projection = lineStart + t * (lineEnd - lineStart); // Projection falls on the segment
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return Vector2.Distance(point, projection);
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}
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/// <summary>
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/// Get the distance between a point and a finite line segment.
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/// </summary>
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/// <remarks>http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment</remarks>
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/// <param name="point">The point.</param>
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/// <param name="lineStart">Line start.</param>
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/// <param name="lineEnd">Line end.</param>
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/// <returns>The distance from point to the nearest point on a line segment.</returns>
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public static float DistancePointLineSegment(Vector3 point, Vector3 lineStart, Vector3 lineEnd)
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{
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// Return minimum distance between line segment vw and point p
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float l2 = ((lineStart.x - lineEnd.x) * (lineStart.x - lineEnd.x)) + ((lineStart.y - lineEnd.y) * (lineStart.y - lineEnd.y)) + ((lineStart.z - lineEnd.z) * (lineStart.z - lineEnd.z)); // i.e. |w-v|^2 - avoid a sqrt
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if (l2 == 0.0f) return Vector3.Distance(point, lineStart); // v == w case
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// Consider the line extending the segment, parameterized as v + t (w - v).
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// We find projection of point p onto the line.
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// It falls where t = [(p-v) . (w-v)] / |w-v|^2
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float t = Vector3.Dot(point - lineStart, lineEnd - lineStart) / l2;
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if (t < 0.0)
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return Vector3.Distance(point, lineStart); // Beyond the 'v' end of the segment
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else if (t > 1.0)
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return Vector3.Distance(point, lineEnd); // Beyond the 'w' end of the segment
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Vector3 projection = lineStart + t * (lineEnd - lineStart); // Projection falls on the segment
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return Vector3.Distance(point, projection);
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}
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/// <summary>
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/// Calculate the nearest point between two rays.
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/// </summary>
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/// <param name="a">First ray.</param>
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/// <param name="b">Second ray.</param>
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/// <returns></returns>
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public static Vector3 GetNearestPointRayRay(Ray a, Ray b)
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{
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return GetNearestPointRayRay(a.origin, a.direction, b.origin, b.direction);
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}
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internal static Vector3 GetNearestPointRayRay(Vector3 ao, Vector3 ad, Vector3 bo, Vector3 bd)
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{
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float dot = Vector3.Dot(ad, bd);
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float abs = Mathf.Abs(dot);
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// ray is parallel (or garbage)
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if ((abs - 1f) > Mathf.Epsilon || abs < Mathf.Epsilon)
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return ao;
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Vector3 c = bo - ao;
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float n = -dot * Vector3.Dot(bd, c) + Vector3.Dot(ad, c) * Vector3.Dot(bd, bd);
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float d = Vector3.Dot(ad, ad) * Vector3.Dot(bd, bd) - dot * dot;
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return ao + ad * (n / d);
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}
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// http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect
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// Returns 1 if the lines intersect, otherwise 0. In addition, if the lines
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// intersect the intersection point may be stored in the intersect var
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internal static bool GetLineSegmentIntersect(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, ref Vector2 intersect)
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{
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intersect = Vector2.zero;
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Vector2 s1, s2;
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s1.x = p1.x - p0.x; s1.y = p1.y - p0.y;
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s2.x = p3.x - p2.x; s2.y = p3.y - p2.y;
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float s, t;
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s = (-s1.y * (p0.x - p2.x) + s1.x * (p0.y - p2.y)) / (-s2.x * s1.y + s1.x * s2.y);
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t = (s2.x * (p0.y - p2.y) - s2.y * (p0.x - p2.x)) / (-s2.x * s1.y + s1.x * s2.y);
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if (s >= 0 && s <= 1 && t >= 0 && t <= 1)
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{
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// Collision detected
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intersect.x = p0.x + (t * s1.x);
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intersect.y = p0.y + (t * s1.y);
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return true;
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}
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return false;
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}
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/// <summary>
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/// True or false lines, do lines intersect.
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/// </summary>
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/// <param name="p0"></param>
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/// <param name="p1"></param>
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/// <param name="p2"></param>
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/// <param name="p3"></param>
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/// <returns></returns>
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internal static bool GetLineSegmentIntersect(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3)
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{
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Vector2 s1, s2;
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s1.x = p1.x - p0.x; s1.y = p1.y - p0.y;
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s2.x = p3.x - p2.x; s2.y = p3.y - p2.y;
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float s, t;
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s = (-s1.y * (p0.x - p2.x) + s1.x * (p0.y - p2.y)) / (-s2.x * s1.y + s1.x * s2.y);
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t = (s2.x * (p0.y - p2.y) - s2.y * (p0.x - p2.x)) / (-s2.x * s1.y + s1.x * s2.y);
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return (s >= 0 && s <= 1 && t >= 0 && t <= 1);
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}
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/// <summary>
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/// Test if a raycast intersects a triangle. Does not test for culling.
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||
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/// </summary>
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||
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/// <remarks>
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||
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/// http://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm
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||
|
|
/// http://www.cs.virginia.edu/~gfx/Courses/2003/ImageSynthesis/papers/Acceleration/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf
|
||
|
|
/// </remarks>
|
||
|
|
/// <param name="InRay"></param>
|
||
|
|
/// <param name="InTriangleA">First vertex position in the triangle.</param>
|
||
|
|
/// <param name="InTriangleB">Second vertex position in the triangle.</param>
|
||
|
|
/// <param name="InTriangleC">Third vertex position in the triangle.</param>
|
||
|
|
/// <param name="OutDistance">If triangle is intersected, this is the distance of intersection point from ray origin. Zero if not intersected.</param>
|
||
|
|
/// <param name="OutPoint">If triangle is intersected, this is the point of collision. Zero if not intersected.</param>
|
||
|
|
/// <returns>True if ray intersects, false if not.</returns>
|
||
|
|
public static bool RayIntersectsTriangle(Ray InRay, Vector3 InTriangleA, Vector3 InTriangleB, Vector3 InTriangleC,
|
||
|
|
out float OutDistance, out Vector3 OutPoint)
|
||
|
|
{
|
||
|
|
OutDistance = 0f;
|
||
|
|
OutPoint = Vector3.zero;
|
||
|
|
|
||
|
|
//Find vectors for two edges sharing V1
|
||
|
|
Vector3 e1 = InTriangleB - InTriangleA;
|
||
|
|
Vector3 e2 = InTriangleC - InTriangleA;
|
||
|
|
|
||
|
|
//Begin calculating determinant - also used to calculate `u` parameter
|
||
|
|
Vector3 P = Vector3.Cross(InRay.direction, e2);
|
||
|
|
|
||
|
|
//if determinant is near zero, ray lies in plane of triangle
|
||
|
|
float det = Vector3.Dot(e1, P);
|
||
|
|
|
||
|
|
// Non-culling branch
|
||
|
|
// {
|
||
|
|
if (det > -Mathf.Epsilon && det < Mathf.Epsilon)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
float inv_det = 1f / det;
|
||
|
|
|
||
|
|
//calculate distance from V1 to ray origin
|
||
|
|
Vector3 T = InRay.origin - InTriangleA;
|
||
|
|
|
||
|
|
// Calculate u parameter and test bound
|
||
|
|
float u = Vector3.Dot(T, P) * inv_det;
|
||
|
|
|
||
|
|
//The intersection lies outside of the triangle
|
||
|
|
if (u < 0f || u > 1f)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
//Prepare to test v parameter
|
||
|
|
Vector3 Q = Vector3.Cross(T, e1);
|
||
|
|
|
||
|
|
//Calculate V parameter and test bound
|
||
|
|
float v = Vector3.Dot(InRay.direction, Q) * inv_det;
|
||
|
|
|
||
|
|
//The intersection lies outside of the triangle
|
||
|
|
if (v < 0f || u + v > 1f)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
float t = Vector3.Dot(e2, Q) * inv_det;
|
||
|
|
// }
|
||
|
|
|
||
|
|
if (t > Mathf.Epsilon)
|
||
|
|
{
|
||
|
|
//ray intersection
|
||
|
|
OutDistance = t;
|
||
|
|
|
||
|
|
OutPoint.x = (u * InTriangleB.x + v * InTriangleC.x + (1 - (u + v)) * InTriangleA.x);
|
||
|
|
OutPoint.y = (u * InTriangleB.y + v * InTriangleC.y + (1 - (u + v)) * InTriangleA.y);
|
||
|
|
OutPoint.z = (u * InTriangleB.z + v * InTriangleC.z + (1 - (u + v)) * InTriangleA.z);
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
// Temporary vector3 values
|
||
|
|
static Vector3 tv1, tv2, tv3, tv4;
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Non-allocating version of Ray / Triangle intersection.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="origin"></param>
|
||
|
|
/// <param name="dir"></param>
|
||
|
|
/// <param name="vert0"></param>
|
||
|
|
/// <param name="vert1"></param>
|
||
|
|
/// <param name="vert2"></param>
|
||
|
|
/// <param name="distance"></param>
|
||
|
|
/// <param name="normal"></param>
|
||
|
|
/// <returns></returns>
|
||
|
|
internal static bool RayIntersectsTriangle2(Vector3 origin,
|
||
|
|
Vector3 dir,
|
||
|
|
Vector3 vert0,
|
||
|
|
Vector3 vert1,
|
||
|
|
Vector3 vert2,
|
||
|
|
out float distance,
|
||
|
|
out Vector3 normal)
|
||
|
|
{
|
||
|
|
Math.Subtract(vert0, vert1, ref tv1);
|
||
|
|
Math.Subtract(vert0, vert2, ref tv2);
|
||
|
|
|
||
|
|
normal = Vector3.Cross(tv1, tv2);
|
||
|
|
distance = 0f;
|
||
|
|
|
||
|
|
// backface culling
|
||
|
|
if (Vector3.Dot(dir, normal) > 0)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
Math.Cross(dir, tv2, ref tv4);
|
||
|
|
float det = Vector3.Dot(tv1, tv4);
|
||
|
|
|
||
|
|
if (det < Mathf.Epsilon)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
Math.Subtract(vert0, origin, ref tv3);
|
||
|
|
|
||
|
|
float u = Vector3.Dot(tv3, tv4);
|
||
|
|
|
||
|
|
if (u < 0f || u > det)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
Math.Cross(tv3, tv1, ref tv4);
|
||
|
|
|
||
|
|
float v = Vector3.Dot(dir, tv4);
|
||
|
|
|
||
|
|
if (v < 0f || u + v > det)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
distance = Vector3.Dot(tv2, tv4) * (1f / det);
|
||
|
|
|
||
|
|
// no hit if point is behind the ray origin
|
||
|
|
return distance > 0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Return the secant of a radian.
|
||
|
|
/// Equivalent to: `1f / cos(x)`.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="x">The radian to calculate the secant of.</param>
|
||
|
|
/// <returns>The secant of radian x.</returns>
|
||
|
|
public static float Secant(float x)
|
||
|
|
{
|
||
|
|
return 1f / Mathf.Cos(x);
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Calculate the unit vector normal of 3 points.
|
||
|
|
/// <br />
|
||
|
|
/// Equivalent to: `B-A x C-A`
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="p0">First point of the triangle.</param>
|
||
|
|
/// <param name="p1">Second point of the triangle.</param>
|
||
|
|
/// <param name="p2">Third point of the triangle.</param>
|
||
|
|
/// <returns></returns>
|
||
|
|
public static Vector3 Normal(Vector3 p0, Vector3 p1, Vector3 p2)
|
||
|
|
{
|
||
|
|
float ax = p1.x - p0.x,
|
||
|
|
ay = p1.y - p0.y,
|
||
|
|
az = p1.z - p0.z,
|
||
|
|
bx = p2.x - p0.x,
|
||
|
|
by = p2.y - p0.y,
|
||
|
|
bz = p2.z - p0.z;
|
||
|
|
|
||
|
|
Vector3 cross = Vector3.zero;
|
||
|
|
|
||
|
|
Cross(ax, ay, az, bx, by, bz, ref cross.x, ref cross.y, ref cross.z);
|
||
|
|
|
||
|
|
if (cross.magnitude < Mathf.Epsilon)
|
||
|
|
{
|
||
|
|
return new Vector3(0f, 0f, 0f); // bad triangle
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
cross.Normalize();
|
||
|
|
return cross;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Get the average normal of a set of individual triangles.
|
||
|
|
/// If p.Length % 3 == 0, finds the normal of each triangle in a face and returns the average. Otherwise return the normal of the first three points.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="p"></param>
|
||
|
|
/// <returns></returns>
|
||
|
|
internal static Vector3 Normal(IList<Vector3> p)
|
||
|
|
{
|
||
|
|
if (p == null || p.Count < 3)
|
||
|
|
return Vector3.zero;
|
||
|
|
|
||
|
|
int c = p.Count;
|
||
|
|
|
||
|
|
if (c % 3 == 0)
|
||
|
|
{
|
||
|
|
Vector3 nrm = Vector3.zero;
|
||
|
|
for (int i = 0; i < c; i += 3)
|
||
|
|
nrm += Normal(p[i + 0], p[i + 1], p[i + 2]);
|
||
|
|
nrm /= (c / 3f);
|
||
|
|
nrm.Normalize();
|
||
|
|
return nrm;
|
||
|
|
}
|
||
|
|
Vector3 cross = Vector3.Cross(p[1] - p[0], p[2] - p[0]);
|
||
|
|
|
||
|
|
if (cross.magnitude < Mathf.Epsilon)
|
||
|
|
return new Vector3(0f, 0f, 0f); // bad triangle
|
||
|
|
|
||
|
|
return cross.normalized;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Gets the average of a vector array.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="array">The array</param>
|
||
|
|
/// <param name="indexes">If provided the average is the sum of all points contained in the indexes array. If not, the entire v array is used.</param>
|
||
|
|
/// <returns>Average Vector3 of passed vertex array.</returns>
|
||
|
|
public static Vector2 Average(IList<Vector2> array, IList<int> indexes = null)
|
||
|
|
{
|
||
|
|
if (array == null)
|
||
|
|
throw new ArgumentNullException("array");
|
||
|
|
|
||
|
|
Vector2 sum = Vector2.zero;
|
||
|
|
float len = indexes == null ? array.Count : indexes.Count;
|
||
|
|
|
||
|
|
if (indexes == null)
|
||
|
|
for (int i = 0; i < len; i++) sum += array[i];
|
||
|
|
else
|
||
|
|
for (int i = 0; i < len; i++) sum += array[indexes[i]];
|
||
|
|
|
||
|
|
return sum / len;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Gets the average of a vector array.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="array">The array.</param>
|
||
|
|
/// <param name="indexes">If provided the average is the sum of all points contained in the indexes array. If not, the entire v array is used.</param>
|
||
|
|
/// <returns>Average Vector3 of passed vertex array.</returns>
|
||
|
|
public static Vector3 Average(IList<Vector3> array, IList<int> indexes = null)
|
||
|
|
{
|
||
|
|
if (array == null)
|
||
|
|
throw new ArgumentNullException("array");
|
||
|
|
|
||
|
|
Vector3 sum = Vector3.zero;
|
||
|
|
|
||
|
|
float len = indexes == null ? array.Count : indexes.Count;
|
||
|
|
|
||
|
|
if (indexes == null)
|
||
|
|
{
|
||
|
|
for (int i = 0; i < len; i++)
|
||
|
|
{
|
||
|
|
sum.x += array[i].x;
|
||
|
|
sum.y += array[i].y;
|
||
|
|
sum.z += array[i].z;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
for (int i = 0; i < len; i++)
|
||
|
|
{
|
||
|
|
sum.x += array[indexes[i]].x;
|
||
|
|
sum.y += array[indexes[i]].y;
|
||
|
|
sum.z += array[indexes[i]].z;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return sum / len;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Average a set of vertices.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="list">The collection from which to select indices.</param>
|
||
|
|
/// <param name="selector">The function used to get vertex values.</param>
|
||
|
|
/// <param name="indexes"></param>
|
||
|
|
/// <typeparam name="T"></typeparam>
|
||
|
|
/// <returns></returns>
|
||
|
|
internal static Vector3 Average<T>(this IList<T> list, Func<T, Vector3> selector, IList<int> indexes = null)
|
||
|
|
{
|
||
|
|
if (list == null)
|
||
|
|
throw new ArgumentNullException("list");
|
||
|
|
|
||
|
|
if (selector == null)
|
||
|
|
throw new ArgumentNullException("selector");
|
||
|
|
|
||
|
|
Vector3 sum = Vector3.zero;
|
||
|
|
float len = indexes == null ? list.Count : indexes.Count;
|
||
|
|
|
||
|
|
if (indexes == null)
|
||
|
|
{
|
||
|
|
for (int i = 0; i < len; i++)
|
||
|
|
sum += selector(list[i]);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
for (int i = 0; i < len; i++)
|
||
|
|
sum += selector(list[indexes[i]]);
|
||
|
|
}
|
||
|
|
|
||
|
|
return sum / len;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Average a set of Vector4.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="v">The collection from which to select indices.</param>
|
||
|
|
/// <param name="indexes">The indexes to use to compute the average value</param>
|
||
|
|
/// <returns>Average Vector4 from selected values</returns>
|
||
|
|
public static Vector4 Average(IList<Vector4> v, IList<int> indexes = null)
|
||
|
|
{
|
||
|
|
if (v == null)
|
||
|
|
throw new ArgumentNullException("v");
|
||
|
|
|
||
|
|
Vector4 sum = Vector4.zero;
|
||
|
|
float len = indexes == null ? v.Count : indexes.Count;
|
||
|
|
if (indexes == null)
|
||
|
|
for (int i = 0; i < len; i++) sum += v[i];
|
||
|
|
else
|
||
|
|
for (int i = 0; i < len; i++) sum += v[indexes[i]];
|
||
|
|
return sum / len;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static Color Average(IList<Color> c, IList<int> indexes = null)
|
||
|
|
{
|
||
|
|
if (c == null)
|
||
|
|
throw new ArgumentNullException("c");
|
||
|
|
|
||
|
|
Color sum = c[0];
|
||
|
|
float len = indexes == null ? c.Count : indexes.Count;
|
||
|
|
if (indexes == null)
|
||
|
|
for (int i = 1; i < len; i++) sum += c[i];
|
||
|
|
else
|
||
|
|
for (int i = 1; i < len; i++) sum += c[indexes[i]];
|
||
|
|
return sum / len;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Compares two Vector2 values component-wise, allowing for a margin of error.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="a">First Vector2 value.</param>
|
||
|
|
/// <param name="b">Second Vector2 value.</param>
|
||
|
|
/// <param name="delta">The maximum difference between components allowed.</param>
|
||
|
|
/// <returns>True if a and b components are respectively within delta distance of one another.</returns>
|
||
|
|
internal static bool Approx2(this Vector2 a, Vector2 b, float delta = k_FltCompareEpsilon)
|
||
|
|
{
|
||
|
|
return
|
||
|
|
Mathf.Abs(a.x - b.x) < delta &&
|
||
|
|
Mathf.Abs(a.y - b.y) < delta;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Compares two Vector3 values component-wise, allowing for a margin of error.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="a">First Vector3 value.</param>
|
||
|
|
/// <param name="b">Second Vector3 value.</param>
|
||
|
|
/// <param name="delta">The maximum difference between components allowed.</param>
|
||
|
|
/// <returns>True if a and b components are respectively within delta distance of one another.</returns>
|
||
|
|
internal static bool Approx3(this Vector3 a, Vector3 b, float delta = k_FltCompareEpsilon)
|
||
|
|
{
|
||
|
|
return
|
||
|
|
Mathf.Abs(a.x - b.x) < delta &&
|
||
|
|
Mathf.Abs(a.y - b.y) < delta &&
|
||
|
|
Mathf.Abs(a.z - b.z) < delta;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Compares two Vector4 values component-wise, allowing for a margin of error.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="a">First Vector4 value.</param>
|
||
|
|
/// <param name="b">Second Vector4 value.</param>
|
||
|
|
/// <param name="delta">The maximum difference between components allowed.</param>
|
||
|
|
/// <returns>True if a and b components are respectively within delta distance of one another.</returns>
|
||
|
|
|
||
|
|
internal static bool Approx4(this Vector4 a, Vector4 b, float delta = k_FltCompareEpsilon)
|
||
|
|
{
|
||
|
|
return
|
||
|
|
Mathf.Abs(a.x - b.x) < delta &&
|
||
|
|
Mathf.Abs(a.y - b.y) < delta &&
|
||
|
|
Mathf.Abs(a.z - b.z) < delta &&
|
||
|
|
Mathf.Abs(a.w - b.w) < delta;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Compares two Color values component-wise, allowing for a margin of error.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="a">First Color value.</param>
|
||
|
|
/// <param name="b">Second Color value.</param>
|
||
|
|
/// <param name="delta">The maximum difference between components allowed.</param>
|
||
|
|
/// <returns>True if a and b components are respectively within delta distance of one another.</returns>
|
||
|
|
internal static bool ApproxC(this Color a, Color b, float delta = k_FltCompareEpsilon)
|
||
|
|
{
|
||
|
|
return Mathf.Abs(a.r - b.r) < delta &&
|
||
|
|
Mathf.Abs(a.g - b.g) < delta &&
|
||
|
|
Mathf.Abs(a.b - b.b) < delta &&
|
||
|
|
Mathf.Abs(a.a - b.a) < delta;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Compares two float values component-wise, allowing for a margin of error.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="a">First float value.</param>
|
||
|
|
/// <param name="b">Second float value.</param>
|
||
|
|
/// <param name="delta">The maximum difference between components allowed.</param>
|
||
|
|
/// <returns>True if a and b components are respectively within delta distance of one another.</returns>
|
||
|
|
|
||
|
|
internal static bool Approx(this float a, float b, float delta = k_FltCompareEpsilon)
|
||
|
|
{
|
||
|
|
return Mathf.Abs(b - a) < Mathf.Abs(delta);
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Wrap value to range.
|
||
|
|
/// </summary>
|
||
|
|
/// <remarks>
|
||
|
|
/// http://stackoverflow.com/questions/707370/clean-efficient-algorithm-for-wrapping-integers-in-c
|
||
|
|
/// </remarks>
|
||
|
|
/// <param name="value"></param>
|
||
|
|
/// <param name="lowerBound"></param>
|
||
|
|
/// <param name="upperBound"></param>
|
||
|
|
/// <returns></returns>
|
||
|
|
internal static int Wrap(int value, int lowerBound, int upperBound)
|
||
|
|
{
|
||
|
|
int range_size = upperBound - lowerBound + 1;
|
||
|
|
|
||
|
|
if (value < lowerBound)
|
||
|
|
value += range_size * ((lowerBound - value) / range_size + 1);
|
||
|
|
|
||
|
|
return lowerBound + (value - lowerBound) % range_size;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Clamp a int to a range.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="value">The value to clamp.</param>
|
||
|
|
/// <param name="lowerBound">The lowest value that the clamped value can be.</param>
|
||
|
|
/// <param name="upperBound">The highest value that the clamped value can be.</param>
|
||
|
|
/// <returns>A value clamped with the range of lowerBound and upperBound.</returns>
|
||
|
|
public static int Clamp(int value, int lowerBound, int upperBound)
|
||
|
|
{
|
||
|
|
return value<lowerBound? lowerBound : value> upperBound ? upperBound : value;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static Vector3 ToSignedMask(this Vector3 vec, float delta = k_FltEpsilon)
|
||
|
|
{
|
||
|
|
return new Vector3(
|
||
|
|
Mathf.Abs(vec.x) > delta ? vec.x / Mathf.Abs(vec.x) : 0f,
|
||
|
|
Mathf.Abs(vec.y) > delta ? vec.y / Mathf.Abs(vec.y) : 0f,
|
||
|
|
Mathf.Abs(vec.z) > delta ? vec.z / Mathf.Abs(vec.z) : 0f
|
||
|
|
);
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static Vector3 Abs(this Vector3 v)
|
||
|
|
{
|
||
|
|
return new Vector3(Mathf.Abs(v.x), Mathf.Abs(v.y), Mathf.Abs(v.z));
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static int IntSum(this Vector3 mask)
|
||
|
|
{
|
||
|
|
return (int)Mathf.Abs(mask.x) + (int)Mathf.Abs(mask.y) + (int)Mathf.Abs(mask.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Non-allocating cross product.
|
||
|
|
/// </summary>
|
||
|
|
/// <remarks>
|
||
|
|
/// `ref` does not box with primitive types (https://msdn.microsoft.com/en-us/library/14akc2c7.aspx)
|
||
|
|
/// </remarks>
|
||
|
|
/// <param name="a"></param>
|
||
|
|
/// <param name="b"></param>
|
||
|
|
/// <param name="x"></param>
|
||
|
|
/// <param name="y"></param>
|
||
|
|
/// <param name="z"></param>
|
||
|
|
internal static void Cross(Vector3 a, Vector3 b, ref float x, ref float y, ref float z)
|
||
|
|
{
|
||
|
|
x = a.y * b.z - a.z * b.y;
|
||
|
|
y = a.z * b.x - a.x * b.z;
|
||
|
|
z = a.x * b.y - a.y * b.x;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Non-allocating cross product.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="a"></param>
|
||
|
|
/// <param name="b"></param>
|
||
|
|
/// <param name="res"></param>
|
||
|
|
internal static void Cross(Vector3 a, Vector3 b, ref Vector3 res)
|
||
|
|
{
|
||
|
|
res.x = a.y * b.z - a.z * b.y;
|
||
|
|
res.y = a.z * b.x - a.x * b.z;
|
||
|
|
res.z = a.x * b.y - a.y * b.x;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Non-allocating cross product.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="ax"></param>
|
||
|
|
/// <param name="ay"></param>
|
||
|
|
/// <param name="az"></param>
|
||
|
|
/// <param name="bx"></param>
|
||
|
|
/// <param name="by"></param>
|
||
|
|
/// <param name="bz"></param>
|
||
|
|
/// <param name="x"></param>
|
||
|
|
/// <param name="y"></param>
|
||
|
|
/// <param name="z"></param>
|
||
|
|
internal static void Cross(float ax, float ay, float az, float bx, float by, float bz, ref float x, ref float y, ref float z)
|
||
|
|
{
|
||
|
|
x = ay * bz - az * by;
|
||
|
|
y = az * bx - ax * bz;
|
||
|
|
z = ax * by - ay * bx;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static void Add(Vector3 a, Vector3 b, ref Vector3 res)
|
||
|
|
{
|
||
|
|
res.x = a.x + b.x;
|
||
|
|
res.y = a.y + b.y;
|
||
|
|
res.z = a.z + b.z;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Vector subtraction without allocating a new vector.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="a"></param>
|
||
|
|
/// <param name="b"></param>
|
||
|
|
/// <param name="res"></param>
|
||
|
|
internal static void Subtract(Vector3 a, Vector3 b, ref Vector3 res)
|
||
|
|
{
|
||
|
|
res.x = b.x - a.x;
|
||
|
|
res.y = b.y - a.y;
|
||
|
|
res.z = b.z - a.z;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static void Divide(Vector3 vector, float value, ref Vector3 res)
|
||
|
|
{
|
||
|
|
res.x = vector.x / value;
|
||
|
|
res.y = vector.y / value;
|
||
|
|
res.z = vector.z / value;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static void Multiply(Vector3 vector, float value, ref Vector3 res)
|
||
|
|
{
|
||
|
|
res.x = vector.x * value;
|
||
|
|
res.y = vector.y * value;
|
||
|
|
res.z = vector.z * value;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static int Min(int a, int b)
|
||
|
|
{
|
||
|
|
return a < b ? a : b;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static int Max(int a, int b)
|
||
|
|
{
|
||
|
|
return a > b ? a : b;
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static bool IsNumber(float value)
|
||
|
|
{
|
||
|
|
return !(float.IsInfinity(value) || float.IsNaN(value));
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static bool IsNumber(Vector2 value)
|
||
|
|
{
|
||
|
|
return IsNumber(value.x) && IsNumber(value.y);
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static bool IsNumber(Vector3 value)
|
||
|
|
{
|
||
|
|
return IsNumber(value.x) && IsNumber(value.y) && IsNumber(value.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static bool IsNumber(Vector4 value)
|
||
|
|
{
|
||
|
|
return IsNumber(value.x) && IsNumber(value.y) && IsNumber(value.z) && IsNumber(value.w);
|
||
|
|
}
|
||
|
|
|
||
|
|
internal static float MakeNonZero(float value, float min = .0001f)
|
||
|
|
{
|
||
|
|
if (float.IsNaN(value) || float.IsInfinity(value) || Mathf.Abs(value) < min)
|
||
|
|
return min * Mathf.Sign(value);
|
||
|
|
return value;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// True if all elements of a vector are equal.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="vector"></param>
|
||
|
|
/// <returns></returns>
|
||
|
|
internal static bool VectorIsUniform(Vector3 vector)
|
||
|
|
{
|
||
|
|
return Mathf.Abs(vector.x - vector.y) < Mathf.Epsilon && Mathf.Abs(vector.x - vector.z) < Mathf.Epsilon;
|
||
|
|
}
|
||
|
|
|
||
|
|
/// <summary>
|
||
|
|
/// Returns a weighted average from values "array", "indices", and a lookup table of index weights.
|
||
|
|
/// </summary>
|
||
|
|
/// <param name="array"></param>
|
||
|
|
/// <param name="indices"></param>
|
||
|
|
/// <param name="weightLookup"></param>
|
||
|
|
/// <returns></returns>
|
||
|
|
internal static Vector3 WeightedAverage(Vector3[] array, IList<int> indices, float[] weightLookup)
|
||
|
|
{
|
||
|
|
if (array == null || indices == null || weightLookup == null) return Vector3.zero;
|
||
|
|
|
||
|
|
float sum = 0f;
|
||
|
|
Vector3 avg = Vector3.zero;
|
||
|
|
|
||
|
|
for (int i = 0; i < indices.Count; i++)
|
||
|
|
{
|
||
|
|
float weight = weightLookup[indices[i]];
|
||
|
|
avg.x += array[indices[i]].x * weight;
|
||
|
|
avg.y += array[indices[i]].y * weight;
|
||
|
|
avg.z += array[indices[i]].z * weight;
|
||
|
|
sum += weight;
|
||
|
|
}
|
||
|
|
return sum > Mathf.Epsilon ? avg /= sum : Vector3.zero;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|