mirror of https://github.com/axmolengine/axmol.git
388 lines
9.6 KiB
C++
388 lines
9.6 KiB
C++
//
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// Copyright (c) 2009-2010 Mikko Mononen memon@inside.org
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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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#include "DetourCommon.h"
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#include "DetourMath.h"
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//////////////////////////////////////////////////////////////////////////////////////////
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void dtClosestPtPointTriangle(float* closest, const float* p,
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const float* a, const float* b, const float* c)
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{
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// Check if P in vertex region outside A
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float ab[3], ac[3], ap[3];
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dtVsub(ab, b, a);
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dtVsub(ac, c, a);
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dtVsub(ap, p, a);
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float d1 = dtVdot(ab, ap);
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float d2 = dtVdot(ac, ap);
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if (d1 <= 0.0f && d2 <= 0.0f)
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{
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// barycentric coordinates (1,0,0)
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dtVcopy(closest, a);
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return;
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}
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// Check if P in vertex region outside B
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float bp[3];
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dtVsub(bp, p, b);
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float d3 = dtVdot(ab, bp);
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float d4 = dtVdot(ac, bp);
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if (d3 >= 0.0f && d4 <= d3)
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{
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// barycentric coordinates (0,1,0)
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dtVcopy(closest, b);
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return;
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}
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// Check if P in edge region of AB, if so return projection of P onto AB
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float vc = d1*d4 - d3*d2;
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if (vc <= 0.0f && d1 >= 0.0f && d3 <= 0.0f)
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{
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// barycentric coordinates (1-v,v,0)
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float v = d1 / (d1 - d3);
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closest[0] = a[0] + v * ab[0];
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closest[1] = a[1] + v * ab[1];
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closest[2] = a[2] + v * ab[2];
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return;
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}
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// Check if P in vertex region outside C
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float cp[3];
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dtVsub(cp, p, c);
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float d5 = dtVdot(ab, cp);
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float d6 = dtVdot(ac, cp);
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if (d6 >= 0.0f && d5 <= d6)
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{
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// barycentric coordinates (0,0,1)
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dtVcopy(closest, c);
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return;
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}
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// Check if P in edge region of AC, if so return projection of P onto AC
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float vb = d5*d2 - d1*d6;
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if (vb <= 0.0f && d2 >= 0.0f && d6 <= 0.0f)
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{
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// barycentric coordinates (1-w,0,w)
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float w = d2 / (d2 - d6);
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closest[0] = a[0] + w * ac[0];
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closest[1] = a[1] + w * ac[1];
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closest[2] = a[2] + w * ac[2];
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return;
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}
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// Check if P in edge region of BC, if so return projection of P onto BC
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float va = d3*d6 - d5*d4;
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if (va <= 0.0f && (d4 - d3) >= 0.0f && (d5 - d6) >= 0.0f)
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{
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// barycentric coordinates (0,1-w,w)
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float w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
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closest[0] = b[0] + w * (c[0] - b[0]);
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closest[1] = b[1] + w * (c[1] - b[1]);
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closest[2] = b[2] + w * (c[2] - b[2]);
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return;
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}
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// P inside face region. Compute Q through its barycentric coordinates (u,v,w)
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float denom = 1.0f / (va + vb + vc);
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float v = vb * denom;
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float w = vc * denom;
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closest[0] = a[0] + ab[0] * v + ac[0] * w;
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closest[1] = a[1] + ab[1] * v + ac[1] * w;
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closest[2] = a[2] + ab[2] * v + ac[2] * w;
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}
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bool dtIntersectSegmentPoly2D(const float* p0, const float* p1,
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const float* verts, int nverts,
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float& tmin, float& tmax,
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int& segMin, int& segMax)
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{
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static const float EPS = 0.000001f;
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tmin = 0;
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tmax = 1;
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segMin = -1;
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segMax = -1;
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float dir[3];
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dtVsub(dir, p1, p0);
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for (int i = 0, j = nverts-1; i < nverts; j=i++)
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{
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float edge[3], diff[3];
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dtVsub(edge, &verts[i*3], &verts[j*3]);
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dtVsub(diff, p0, &verts[j*3]);
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const float n = dtVperp2D(edge, diff);
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const float d = dtVperp2D(dir, edge);
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if (fabsf(d) < EPS)
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{
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// S is nearly parallel to this edge
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if (n < 0)
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return false;
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else
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continue;
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}
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const float t = n / d;
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if (d < 0)
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{
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// segment S is entering across this edge
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if (t > tmin)
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{
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tmin = t;
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segMin = j;
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// S enters after leaving polygon
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if (tmin > tmax)
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return false;
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}
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}
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else
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{
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// segment S is leaving across this edge
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if (t < tmax)
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{
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tmax = t;
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segMax = j;
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// S leaves before entering polygon
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if (tmax < tmin)
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return false;
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}
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}
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}
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return true;
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}
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float dtDistancePtSegSqr2D(const float* pt, const float* p, const float* q, float& t)
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{
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float pqx = q[0] - p[0];
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float pqz = q[2] - p[2];
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float dx = pt[0] - p[0];
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float dz = pt[2] - p[2];
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float d = pqx*pqx + pqz*pqz;
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t = pqx*dx + pqz*dz;
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if (d > 0) t /= d;
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if (t < 0) t = 0;
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else if (t > 1) t = 1;
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dx = p[0] + t*pqx - pt[0];
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dz = p[2] + t*pqz - pt[2];
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return dx*dx + dz*dz;
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}
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void dtCalcPolyCenter(float* tc, const unsigned short* idx, int nidx, const float* verts)
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{
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tc[0] = 0.0f;
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tc[1] = 0.0f;
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tc[2] = 0.0f;
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for (int j = 0; j < nidx; ++j)
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{
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const float* v = &verts[idx[j]*3];
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tc[0] += v[0];
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tc[1] += v[1];
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tc[2] += v[2];
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}
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const float s = 1.0f / nidx;
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tc[0] *= s;
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tc[1] *= s;
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tc[2] *= s;
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}
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bool dtClosestHeightPointTriangle(const float* p, const float* a, const float* b, const float* c, float& h)
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{
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const float EPS = 1e-6f;
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float v0[3], v1[3], v2[3];
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dtVsub(v0, c, a);
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dtVsub(v1, b, a);
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dtVsub(v2, p, a);
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// Compute scaled barycentric coordinates
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float denom = v0[0] * v1[2] - v0[2] * v1[0];
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if (fabsf(denom) < EPS)
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return false;
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float u = v1[2] * v2[0] - v1[0] * v2[2];
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float v = v0[0] * v2[2] - v0[2] * v2[0];
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if (denom < 0) {
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denom = -denom;
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u = -u;
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v = -v;
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}
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// If point lies inside the triangle, return interpolated ycoord.
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if (u >= 0.0f && v >= 0.0f && (u + v) <= denom) {
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h = a[1] + (v0[1] * u + v1[1] * v) / denom;
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return true;
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}
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return false;
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}
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/// @par
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///
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/// All points are projected onto the xz-plane, so the y-values are ignored.
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bool dtPointInPolygon(const float* pt, const float* verts, const int nverts)
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{
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// TODO: Replace pnpoly with triArea2D tests?
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int i, j;
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bool c = false;
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for (i = 0, j = nverts-1; i < nverts; j = i++)
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{
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const float* vi = &verts[i*3];
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const float* vj = &verts[j*3];
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if (((vi[2] > pt[2]) != (vj[2] > pt[2])) &&
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(pt[0] < (vj[0]-vi[0]) * (pt[2]-vi[2]) / (vj[2]-vi[2]) + vi[0]) )
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c = !c;
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}
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return c;
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}
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bool dtDistancePtPolyEdgesSqr(const float* pt, const float* verts, const int nverts,
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float* ed, float* et)
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{
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// TODO: Replace pnpoly with triArea2D tests?
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int i, j;
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bool c = false;
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for (i = 0, j = nverts-1; i < nverts; j = i++)
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{
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const float* vi = &verts[i*3];
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const float* vj = &verts[j*3];
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if (((vi[2] > pt[2]) != (vj[2] > pt[2])) &&
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(pt[0] < (vj[0]-vi[0]) * (pt[2]-vi[2]) / (vj[2]-vi[2]) + vi[0]) )
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c = !c;
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ed[j] = dtDistancePtSegSqr2D(pt, vj, vi, et[j]);
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}
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return c;
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}
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static void projectPoly(const float* axis, const float* poly, const int npoly,
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float& rmin, float& rmax)
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{
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rmin = rmax = dtVdot2D(axis, &poly[0]);
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for (int i = 1; i < npoly; ++i)
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{
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const float d = dtVdot2D(axis, &poly[i*3]);
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rmin = dtMin(rmin, d);
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rmax = dtMax(rmax, d);
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}
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}
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inline bool overlapRange(const float amin, const float amax,
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const float bmin, const float bmax,
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const float eps)
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{
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return ((amin+eps) > bmax || (amax-eps) < bmin) ? false : true;
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}
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/// @par
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///
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/// All vertices are projected onto the xz-plane, so the y-values are ignored.
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bool dtOverlapPolyPoly2D(const float* polya, const int npolya,
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const float* polyb, const int npolyb)
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{
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const float eps = 1e-4f;
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for (int i = 0, j = npolya-1; i < npolya; j=i++)
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{
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const float* va = &polya[j*3];
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const float* vb = &polya[i*3];
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const float n[3] = { vb[2]-va[2], 0, -(vb[0]-va[0]) };
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float amin,amax,bmin,bmax;
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projectPoly(n, polya, npolya, amin,amax);
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projectPoly(n, polyb, npolyb, bmin,bmax);
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if (!overlapRange(amin,amax, bmin,bmax, eps))
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{
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// Found separating axis
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return false;
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}
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}
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for (int i = 0, j = npolyb-1; i < npolyb; j=i++)
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{
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const float* va = &polyb[j*3];
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const float* vb = &polyb[i*3];
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const float n[3] = { vb[2]-va[2], 0, -(vb[0]-va[0]) };
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float amin,amax,bmin,bmax;
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projectPoly(n, polya, npolya, amin,amax);
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projectPoly(n, polyb, npolyb, bmin,bmax);
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if (!overlapRange(amin,amax, bmin,bmax, eps))
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{
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// Found separating axis
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return false;
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}
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}
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return true;
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}
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// Returns a random point in a convex polygon.
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// Adapted from Graphics Gems article.
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void dtRandomPointInConvexPoly(const float* pts, const int npts, float* areas,
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const float s, const float t, float* out)
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{
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// Calc triangle araes
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float areasum = 0.0f;
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for (int i = 2; i < npts; i++) {
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areas[i] = dtTriArea2D(&pts[0], &pts[(i-1)*3], &pts[i*3]);
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areasum += dtMax(0.001f, areas[i]);
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}
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// Find sub triangle weighted by area.
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const float thr = s*areasum;
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float acc = 0.0f;
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float u = 1.0f;
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int tri = npts - 1;
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for (int i = 2; i < npts; i++) {
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const float dacc = areas[i];
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if (thr >= acc && thr < (acc+dacc))
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{
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u = (thr - acc) / dacc;
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tri = i;
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break;
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}
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acc += dacc;
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}
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float v = dtMathSqrtf(t);
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const float a = 1 - v;
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const float b = (1 - u) * v;
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const float c = u * v;
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const float* pa = &pts[0];
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const float* pb = &pts[(tri-1)*3];
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const float* pc = &pts[tri*3];
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out[0] = a*pa[0] + b*pb[0] + c*pc[0];
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out[1] = a*pa[1] + b*pb[1] + c*pc[1];
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out[2] = a*pa[2] + b*pb[2] + c*pc[2];
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}
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inline float vperpXZ(const float* a, const float* b) { return a[0]*b[2] - a[2]*b[0]; }
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bool dtIntersectSegSeg2D(const float* ap, const float* aq,
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const float* bp, const float* bq,
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float& s, float& t)
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{
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float u[3], v[3], w[3];
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dtVsub(u,aq,ap);
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dtVsub(v,bq,bp);
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dtVsub(w,ap,bp);
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float d = vperpXZ(u,v);
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if (fabsf(d) < 1e-6f) return false;
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s = vperpXZ(v,w) / d;
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t = vperpXZ(u,w) / d;
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return true;
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}
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