CWE-ou-minkata/Sources/Plasma/PubUtilLib/plMath/plTriUtils.cpp

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#include "HeadSpin.h"
#include "hsGeometry3.h"
#include <cmath>
#include "plTriUtils.h"

static const float kAlmostZero = 1.e-5f;
static const float kPastZero = -kAlmostZero;
static const float kPastOne = 1.f + kAlmostZero;
static const float kAlmostOne = 1.f - kAlmostZero;
static const float kAlmostZeroSquared = kAlmostZero*kAlmostZero;

static inline hsVector3 Cross(const hsScalarTriple& p0, const hsScalarTriple& p1)
{
    return hsVector3(p0.fY * p1.fZ - p0.fZ * p1.fY, 
                    p0.fZ * p1.fX - p0.fX * p1.fZ, 
                    p0.fX * p1.fY - p0.fY * p1.fX);
}


// There's actually a possibly faster way to do all this.
// The barycentric coordinate in 3-space is the same as the barycentric coordinate of the projection
// in 2-space, as long as the projection doesn't degenerate the triangle (i.e. project the tri onto
// a plane perpindicular to the tri). The tri can't be perpindicular to all three major axes, so by
// picking the right one (or just not picking the wrong one), the lengths of the cross products becomes
// just the z component (e.g. v0.x*v1.y - v0.y*v1.x), so all the square roots go away (not to mention all
// the vector math going from 3 component to 2).
plTriUtils::Bary plTriUtils::ComputeBarycentricProjection(const hsPoint3& p0, const hsPoint3& p1, const hsPoint3& p2, hsPoint3&p, hsPoint3& out)
{
    hsVector3 v12(&p1, &p2);
    hsVector3 v02(&p0, &p2);
    hsVector3 norm = Cross(v12, v02);

    float invLenSq12 = norm.MagnitudeSquared();
    if( invLenSq12 < kAlmostZero )
        return kDegenerateTri; // degenerate triangle

    invLenSq12 = 1.f / invLenSq12;

    p += norm * (hsVector3(&p2, &p).InnerProduct(norm) * invLenSq12);

    hsVector3 vp2(&p, &p2);
    hsVector3 v0 = Cross(v12, vp2);
    hsVector3 v1 = Cross(vp2, v02);

    return IComputeBarycentric(norm, invLenSq12, v0, v1, out);
}

plTriUtils::Bary plTriUtils::ComputeBarycentric(const hsPoint3& p0, const hsPoint3& p1, const hsPoint3& p2, const hsPoint3&p, hsPoint3& out)
{
    hsVector3 v12(&p1, &p2);
    hsVector3 v02(&p0, &p2);
    hsVector3 norm = Cross(v12, v02);
    float invLenSq12 = norm.MagnitudeSquared();
    if( invLenSq12 < kAlmostZero )
        return kDegenerateTri; // degenerate triangle

    invLenSq12 = 1.f / invLenSq12;

    hsVector3 vp2(&p, &p2);
    hsVector3 v0 = Cross(v12, vp2);
    hsVector3 v1 = Cross(vp2, v02);

    return IComputeBarycentric(norm, invLenSq12, v0, v1, out);
}


plTriUtils::Bary plTriUtils::IComputeBarycentric(const hsVector3& v12, float invLenSq12, const hsVector3& v0, const hsVector3& v1, hsPoint3& out)
{
    uint32_t  state = 0;

    float lenSq0 = v0.MagnitudeSquared();
    if( lenSq0 < kAlmostZeroSquared )
    {
        // On edge p1-p2;
        out[0] = 0;
        state |= kOnEdge12;
    }
    else
    {
        out[0] = lenSq0 * invLenSq12;
        out[0] = sqrt(out[0]);
        // 
        if( v0.InnerProduct(v12) < 0 )
        {
            out[0] = -out[0];
            state |= kOutsideTri;
        }
        else if( out[0] > kPastOne )
            state |= kOutsideTri;
        else if( out[0] > kAlmostOne )
            state |= kOnVertex0;
    }
    
    float lenSq1 = v1.MagnitudeSquared();
    if( lenSq1 < kAlmostZeroSquared )
    {
        // On edge p0-p2
        out[1] = 0;
        state |= kOnEdge02;
    }
    else
    {
        out[1] = lenSq1 * invLenSq12;
        out[1] = sqrt(out[1]);

        if( v1.InnerProduct(v12) < 0 )
        {
            out[1] = -out[1];
            state |= kOutsideTri;
        }
        else if( out[1] > kPastOne )
            state |= kOutsideTri;
        else if( out[1] > kAlmostOne )
            state |= kOnVertex1;
    }

    // Could make more robust against precision problems
    // by repeating above for out[2], then normalizing
    // so sum(out[i]) = 1.f
    out[2] = 1.f - out[0] - out[1];

    if( out[2] < kPastZero )
        state |= kOutsideTri;
    else if( out[2] < kAlmostZero )
        state |= kOnEdge01;
    else if( out[2] > kAlmostOne )
        state |= kOnVertex2;

    /*
    if( a,b,c outside range [0..1] )
        p is outside tri;
    else if( a,b,c == 1 )
        p is on vert;
    else if( a,b,c == 0 )
        p is on edge;
    */

    if( state & kOutsideTri )
        return kOutsideTri;

    if( state & kOnVertex )
        return Bary(state & kOnVertex);

    if( state & kOnEdge )
        return Bary(state & kOnEdge);

    return kInsideTri;
}

//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
int plTriUtils::ISelectAxis(const hsVector3& norm)
{
    int retVal = -2;
    float maxDim = 0;
    int i;
    for( i = 0; i < 3; i++ )
    {
        if( norm[i] > maxDim )
        {
            maxDim = norm[i];
            retVal = i;
        }
        else if( -norm[i] > maxDim )
        {
            maxDim = -norm[i];
            retVal = i;
        }
    }
    return retVal;
}

bool plTriUtils::IFastBarycentric(int iAx, const hsPoint3& p0, const hsPoint3& p1, const hsPoint3& p2, const hsPoint3&p, hsPoint3& out)
{
    if( --iAx < 0 )
        iAx = 2;
    int jAx = iAx - 1;
    if( jAx < 0 )
        jAx = 2;

    hsVector3 v02(&p0, &p2);
    hsVector3 v12(&p1, &p2);

    float totArea = v02[iAx] * v12[jAx] - v02[jAx] * v12[iAx];
    hsAssert(totArea != 0, "Should have already filtered degerate tris and degenerate projection");
    
    float invTotArea = 1.f / totArea;

    hsVector3 vp2(&p, &p2);

    float aArea = vp2[iAx] * v12[jAx] - vp2[jAx] * v12[iAx];

    float bArea = v02[iAx] * vp2[jAx] - v02[jAx] * vp2[iAx];

    out[0] = aArea * invTotArea;
    out[1] = bArea * invTotArea;
    out[2] = 1.f - out[0] - out[1];

    return true;
}

bool plTriUtils::FastBarycentricProjection(const hsPoint3& p0, const hsPoint3& p1, const hsPoint3& p2, hsPoint3&p, hsPoint3& out)
{
    hsVector3 v02(&p0, &p2);
    hsVector3 v12(&p1, &p2);

    hsVector3 norm = Cross(v12, v02);
    float invLenSq12 = norm.MagnitudeSquared();
    if( invLenSq12 < kAlmostZero )
        return false; // degenerate triangle

    invLenSq12 = 1.f / invLenSq12;

    hsVector3 del(&p0, &p);
    float delDotNormOverLenSq = del.InnerProduct(norm) * invLenSq12;

    p += norm * delDotNormOverLenSq;

    int iAx = ISelectAxis(norm);
    hsAssert(iAx >= 0, "Should have already picked out degenerate tris");

    return IFastBarycentric(iAx, p0, p1, p2, p, out);
}

bool plTriUtils::FastBarycentric(const hsPoint3& p0, const hsPoint3& p1, const hsPoint3& p2, const hsPoint3&p, hsPoint3& out)
{
    hsVector3 v02(&p0, &p2);
    hsVector3 v12(&p1, &p2);
    int iAx = ISelectAxis(Cross(v12, v02));
    if( iAx < 0 )
        return false;
    return IFastBarycentric(iAx, p0, p1, p2, p, out);
}

//////////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////////
bool plTriUtils::ProjectOntoPlane(const hsVector3& norm, float dist, hsPoint3& p)
{
    float normMagSq = norm.MagnitudeSquared();
    if( normMagSq > kAlmostZero )
    {
        dist /= normMagSq;

        p += norm * dist;

        return true;
    }
    return false;
}

bool plTriUtils::ProjectOntoPlane(const hsPoint3& p0, const hsPoint3& p1, const hsPoint3& p2, hsPoint3& p)
{
    hsVector3 v02(&p0, &p2);
    hsVector3 v12(&p1, &p2);

    hsVector3 norm = v12 % v02;

    float dist = norm.InnerProduct(p0 - p);

    return ProjectOntoPlane(norm, dist, p);
}

bool plTriUtils::ProjectOntoPlaneAlongVector(const hsVector3& norm, float dist, const hsVector3& vec, hsPoint3& p)
{
    float s = norm.InnerProduct(vec);
    const float kAlmostZero = 1.e-5f;
    if( (s > kAlmostZero)||(s < kPastZero) )
    {
        dist /= s;

        p += vec * dist;

        return true;
    }
    return false;
}

bool plTriUtils::ProjectOntoPlaneAlongVector(const hsPoint3& p0, const hsPoint3& p1, const hsPoint3& p2, const hsVector3& vec, hsPoint3& p)
{
    hsVector3 v02(&p0, &p2);
    hsVector3 v12(&p1, &p2);

    hsVector3 norm = v12 % v02;
    float dist = norm.InnerProduct(p0 - p);

    return ProjectOntoPlaneAlongVector(norm, dist, vec, p);
}