/* The MIT License * * Copyright (c) 2010 Intel Corporation. * All rights reserved. * * Based on the convexdecomposition library from * <http://codesuppository.googlecode.com> by John W. Ratcliff and Stan Melax. * * Permission is hereby granted, free of charge, to any person obtaining a copy * of this software and associated documentation files (the "Software"), to deal * in the Software without restriction, including without limitation the rights * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the Software is * furnished to do so, subject to the following conditions: * * The above copyright notice and this permission notice shall be included in * all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN * THE SOFTWARE. */ using System; namespace OpenSim.Region.PhysicsModules.ConvexDecompositionDotNet { public class float3 : IEquatable<float3> { public float x; public float y; public float z; public float3() { x = 0; y = 0; z = 0; } public float3(float _x, float _y, float _z) { x = _x; y = _y; z = _z; } public float3(float3 f) { x = f.x; y = f.y; z = f.z; } public float this[int i] { get { switch (i) { case 0: return x; case 1: return y; case 2: return z; } throw new ArgumentOutOfRangeException(); } } public float Distance(float3 a) { float3 d = new float3(a.x - x, a.y - y, a.z - z); return d.Length(); } public float Distance2(float3 a) { float dx = a.x - x; float dy = a.y - y; float dz = a.z - z; return dx * dx + dy * dy + dz * dz; } public float Length() { return (float)Math.Sqrt(x * x + y * y + z * z); } public float Area(float3 p1, float3 p2) { float A = Partial(p1); A += p1.Partial(p2); A += p2.Partial(this); return A * 0.5f; } public float Partial(float3 p) { return (x * p.y) - (p.x * y); } // Given a point and a line (defined by two points), compute the closest point // in the line. (The line is treated as infinitely long.) public void NearestPointInLine(float3 point, float3 line0, float3 line1) { float3 nearestPoint = new float3(); float3 lineDelta = line1 - line0; // Handle degenerate lines if (lineDelta == float3.Zero) { nearestPoint = line0; } else { float delta = float3.dot(point - line0, lineDelta) / float3.dot(lineDelta, lineDelta); nearestPoint = line0 + lineDelta * delta; } this.x = nearestPoint.x; this.y = nearestPoint.y; this.z = nearestPoint.z; } // Given a point and a line segment (defined by two points), compute the closest point // in the line. Cap the point at the endpoints of the line segment. public void NearestPointInLineSegment(float3 point, float3 line0, float3 line1) { float3 nearestPoint = new float3(); float3 lineDelta = line1 - line0; // Handle degenerate lines if (lineDelta == Zero) { nearestPoint = line0; } else { float delta = float3.dot(point - line0, lineDelta) / float3.dot(lineDelta, lineDelta); // Clamp the point to conform to the segment's endpoints if (delta < 0) delta = 0; else if (delta > 1) delta = 1; nearestPoint = line0 + lineDelta * delta; } this.x = nearestPoint.x; this.y = nearestPoint.y; this.z = nearestPoint.z; } // Given a point and a triangle (defined by three points), compute the closest point // in the triangle. Clamp the point so it's confined to the area of the triangle. public void NearestPointInTriangle(float3 point, float3 triangle0, float3 triangle1, float3 triangle2) { float3 nearestPoint = new float3(); float3 lineDelta0 = triangle1 - triangle0; float3 lineDelta1 = triangle2 - triangle0; // Handle degenerate triangles if ((lineDelta0 == Zero) || (lineDelta1 == Zero)) { nearestPoint.NearestPointInLineSegment(point, triangle1, triangle2); } else if (lineDelta0 == lineDelta1) { nearestPoint.NearestPointInLineSegment(point, triangle0, triangle1); } else { float3[] axis = new float3[3] { new float3(), new float3(), new float3() }; axis[0].NearestPointInLine(triangle0, triangle1, triangle2); axis[1].NearestPointInLine(triangle1, triangle0, triangle2); axis[2].NearestPointInLine(triangle2, triangle0, triangle1); float3 axisDot = new float3(); axisDot.x = dot(triangle0 - axis[0], point - axis[0]); axisDot.y = dot(triangle1 - axis[1], point - axis[1]); axisDot.z = dot(triangle2 - axis[2], point - axis[2]); bool bForce = true; float bestMagnitude2 = 0; float closeMagnitude2; float3 closePoint = new float3(); if (axisDot.x < 0f) { closePoint.NearestPointInLineSegment(point, triangle1, triangle2); closeMagnitude2 = point.Distance2(closePoint); if (bForce || (bestMagnitude2 > closeMagnitude2)) { bForce = false; bestMagnitude2 = closeMagnitude2; nearestPoint = closePoint; } } if (axisDot.y < 0f) { closePoint.NearestPointInLineSegment(point, triangle0, triangle2); closeMagnitude2 = point.Distance2(closePoint); if (bForce || (bestMagnitude2 > closeMagnitude2)) { bForce = false; bestMagnitude2 = closeMagnitude2; nearestPoint = closePoint; } } if (axisDot.z < 0f) { closePoint.NearestPointInLineSegment(point, triangle0, triangle1); closeMagnitude2 = point.Distance2(closePoint); if (bForce || (bestMagnitude2 > closeMagnitude2)) { bForce = false; bestMagnitude2 = closeMagnitude2; nearestPoint = closePoint; } } // If bForce is true at this point, it means the nearest point lies // inside the triangle; use the nearest-point-on-a-plane equation if (bForce) { float3 normal; // Get the normal of the polygon (doesn't have to be a unit vector) normal = float3.cross(lineDelta0, lineDelta1); float3 pointDelta = point - triangle0; float delta = float3.dot(normal, pointDelta) / float3.dot(normal, normal); nearestPoint = point - normal * delta; } } this.x = nearestPoint.x; this.y = nearestPoint.y; this.z = nearestPoint.z; } public static float3 operator +(float3 a, float3 b) { return new float3(a.x + b.x, a.y + b.y, a.z + b.z); } public static float3 operator -(float3 a, float3 b) { return new float3(a.x - b.x, a.y - b.y, a.z - b.z); } public static float3 operator -(float3 a, float s) { return new float3(a.x - s, a.y - s, a.z - s); } public static float3 operator -(float3 v) { return new float3(-v.x, -v.y, -v.z); } public static float3 operator *(float3 v, float s) { return new float3(v.x * s, v.y * s, v.z * s); } public static float3 operator *(float s, float3 v) { return new float3(v.x * s, v.y * s, v.z * s); } public static float3 operator *(float3 v, float3x3 m) { return new float3((m.x.x * v.x + m.y.x * v.y + m.z.x * v.z), (m.x.y * v.x + m.y.y * v.y + m.z.y * v.z), (m.x.z * v.x + m.y.z * v.y + m.z.z * v.z)); } public static float3 operator *(float3x3 m, float3 v) { return new float3(dot(m.x, v), dot(m.y, v), dot(m.z, v)); } public static float3 operator /(float3 v, float s) { float sinv = 1.0f / s; return new float3(v.x * sinv, v.y * sinv, v.z * sinv); } public bool Equals(float3 other) { return this == other; } public override bool Equals(object obj) { float3 f = obj as float3; if (f == null) return false; return this == f; } public override int GetHashCode() { return x.GetHashCode() ^ y.GetHashCode() ^ z.GetHashCode(); } public static bool operator ==(float3 a, float3 b) { // If both are null, or both are same instance, return true. if (System.Object.ReferenceEquals(a, b)) return true; // If one is null, but not both, return false. if (((object)a == null) || ((object)b == null)) return false; return (a.x == b.x && a.y == b.y && a.z == b.z); } public static bool operator !=(float3 a, float3 b) { return (a.x != b.x || a.y != b.y || a.z != b.z); } public static float dot(float3 a, float3 b) { return a.x * b.x + a.y * b.y + a.z * b.z; } public static float3 cmul(float3 v1, float3 v2) { return new float3(v1.x * v2.x, v1.y * v2.y, v1.z * v2.z); } public static float3 cross(float3 a, float3 b) { return new float3(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x); } public static float3 Interpolate(float3 v0, float3 v1, float alpha) { return v0 * (1 - alpha) + v1 * alpha; } public static float3 Round(float3 a, int digits) { return new float3((float)Math.Round(a.x, digits), (float)Math.Round(a.y, digits), (float)Math.Round(a.z, digits)); } public static float3 VectorMax(float3 a, float3 b) { return new float3(Math.Max(a.x, b.x), Math.Max(a.y, b.y), Math.Max(a.z, b.z)); } public static float3 VectorMin(float3 a, float3 b) { return new float3(Math.Min(a.x, b.x), Math.Min(a.y, b.y), Math.Min(a.z, b.z)); } public static float3 vabs(float3 v) { return new float3(Math.Abs(v.x), Math.Abs(v.y), Math.Abs(v.z)); } public static float magnitude(float3 v) { return (float)Math.Sqrt(v.x * v.x + v.y * v.y + v.z * v.z); } public static float3 normalize(float3 v) { float d = magnitude(v); if (d == 0) d = 0.1f; d = 1 / d; return new float3(v.x * d, v.y * d, v.z * d); } public static float3 safenormalize(float3 v) { if (magnitude(v) <= 0.0f) return new float3(1, 0, 0); else return normalize(v); } public static float Yaw(float3 v) { return (v.y == 0.0 && v.x == 0.0) ? 0.0f : (float)Math.Atan2(-v.x, v.y) * (180.0f / 3.14159264f); } public static float Pitch(float3 v) { return (float)Math.Atan2(v.z, Math.Sqrt(v.x * v.x + v.y * v.y)) * (180.0f / 3.14159264f); } public float ComputePlane(float3 A, float3 B, float3 C) { float vx, vy, vz, wx, wy, wz, vw_x, vw_y, vw_z, mag; vx = (B.x - C.x); vy = (B.y - C.y); vz = (B.z - C.z); wx = (A.x - B.x); wy = (A.y - B.y); wz = (A.z - B.z); vw_x = vy * wz - vz * wy; vw_y = vz * wx - vx * wz; vw_z = vx * wy - vy * wx; mag = (float)Math.Sqrt((vw_x * vw_x) + (vw_y * vw_y) + (vw_z * vw_z)); if (mag < 0.000001f) { mag = 0; } else { mag = 1.0f / mag; } x = vw_x * mag; y = vw_y * mag; z = vw_z * mag; float D = 0.0f - ((x * A.x) + (y * A.y) + (z * A.z)); return D; } public override string ToString() { return String.Format("<{0}, {1}, {2}>", x, y, z); } public static readonly float3 Zero = new float3(); } }