126 lines
3.3 KiB
C
126 lines
3.3 KiB
C
/*
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* Copyright (c) 2016-2016 Irlan Robson http://www.irlan.net
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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#ifndef B3_GEOMETRY_H
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#define B3_GEOMETRY_H
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#include <bounce/common/math/math.h>
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#include <bounce/common/math/transform.h>
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// A plane in constant normal form.
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// dot(n, p) - d = 0.
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struct b3Plane
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{
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// Does nothing for performance.
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b3Plane() { }
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// Set this plane from a normal and a signed distance from its origin.
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b3Plane(const b3Vec3& _normal, float32 _offset)
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{
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normal = _normal;
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offset = _offset;
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}
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// Set this plane from a normal and a point on the plane.
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b3Plane(const b3Vec3& _normal, const b3Vec3& _point)
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{
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normal = _normal;
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offset = b3Dot(_normal, _point);
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}
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// Compute this plane from three non-colinear points.
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b3Plane(const b3Vec3& A, const b3Vec3& B, const b3Vec3& C)
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{
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b3Vec3 N = b3Cross(B - A, C - A);
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normal = b3Normalize(N);
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offset = b3Dot(normal, A);
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}
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b3Vec3 normal;
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float32 offset;
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};
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// Transform a plane by a given frame.
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inline b3Plane operator*(const b3Transform& T, const b3Plane& plane)
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{
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b3Vec3 normal = b3Mul(T.rotation, plane.normal);
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return b3Plane(normal, plane.offset + b3Dot(normal, T.position));
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}
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// Transform a plane by a given frame.
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inline b3Plane b3Mul(const b3Transform& T, const b3Plane& plane)
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{
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b3Vec3 normal = b3Mul(T.rotation, plane.normal);
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return b3Plane(normal, plane.offset + b3Dot(normal, T.position));
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}
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// Compute the distance between a point and a plane.
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inline float32 b3Distance(const b3Vec3& P, const b3Plane& plane)
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{
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return b3Dot(plane.normal, P) - plane.offset;
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}
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// Project a point onto a normal plane.
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inline b3Vec3 b3ClosestPointOnPlane(const b3Vec3& P, const b3Plane& plane)
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{
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float32 fraction = b3Distance(P, plane);
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return P - fraction * plane.normal;
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}
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// Convert a point Q from euclidean coordinates to barycentric coordinates (u, v)
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// with respect to a segment AB.
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// The last output value is the divisor.
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inline void b3BarycentricCoordinates(float32 out[3],
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const b3Vec3& A, const b3Vec3& B,
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const b3Vec3& Q)
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{
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b3Vec3 AB = B - A;
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b3Vec3 QA = A - Q;
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b3Vec3 QB = B - Q;
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float32 divisor = b3Dot(AB, AB);
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out[0] = b3Dot(QB, AB);
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out[1] = -b3Dot(QA, AB);
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out[2] = divisor;
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}
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// Project a point onto a segment AB.
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inline b3Vec3 b3ClosestPointOnSegment(const b3Vec3& P, const b3Vec3& A, const b3Vec3& B)
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{
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float32 wAB[3];
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b3BarycentricCoordinates(wAB, A, B, P);
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if (wAB[1] <= 0.0f)
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{
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return A;
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}
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if (wAB[0] <= 0.0f)
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{
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return B;
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}
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float32 s = 1.0f / wAB[2];
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float32 wA = s * wAB[0];
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float32 wB = s * wAB[1];
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return wA * A + wB * B;
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}
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#endif
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