IceTriangle.cpp

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// Precompiled Header
#include "Stdafx.h"


using namespace Opcode;



static sdword VPlaneSideEps(const Point& v, const Plane& plane, float epsilon)
{
    // Compute distance from current vertex to the plane
    float Dist = plane.Distance(v);
    // Compute side:
    // 1    = the vertex is on the positive side of the plane
    // -1   = the vertex is on the negative side of the plane
    // 0    = the vertex is on the plane (within epsilon)
    return Dist > epsilon ? 1 : Dist < -epsilon ? -1 : 0;
}


void Triangle::Flip()
{
    Point Tmp = mVerts[1];
    mVerts[1] = mVerts[2];
    mVerts[2] = Tmp;
}


float Triangle::Area() const
{
    const Point& p0 = mVerts[0];
    const Point& p1 = mVerts[1];
    const Point& p2 = mVerts[2];
    return ((p0 - p1)^(p0 - p2)).Magnitude() * 0.5f;
}


float Triangle::Perimeter() const
{
    const Point& p0 = mVerts[0];
    const Point& p1 = mVerts[1];
    const Point& p2 = mVerts[2];
    return      p0.Distance(p1)
            +   p0.Distance(p2)
            +   p1.Distance(p2);
}


float Triangle::Compacity() const
{
    float P = Perimeter();
    if(P==0.0f) return 0.0f;
    return (4.0f*PI*Area()/(P*P));
}


void Triangle::Normal(Point& normal) const
{
    const Point& p0 = mVerts[0];
    const Point& p1 = mVerts[1];
    const Point& p2 = mVerts[2];
    normal = ((p0 - p1)^(p0 - p2)).Normalize();
}


void Triangle::DenormalizedNormal(Point& normal) const
{
    const Point& p0 = mVerts[0];
    const Point& p1 = mVerts[1];
    const Point& p2 = mVerts[2];
    normal = ((p0 - p1)^(p0 - p2));
}


void Triangle::Center(Point& center) const
{
    const Point& p0 = mVerts[0];
    const Point& p1 = mVerts[1];
    const Point& p2 = mVerts[2];
    center = (p0 + p1 + p2)*INV3;
}

PartVal Triangle::TestAgainstPlane(const Plane& plane, float epsilon) const
{
    bool Pos = false, Neg = false;

    // Loop through all vertices
    for(udword i=0;i<3;i++)
    {
        // Compute side:
        sdword Side = VPlaneSideEps(mVerts[i], plane, epsilon);

                if (Side < 0)   Neg = true;
        else    if (Side > 0)   Pos = true;
    }

            if (!Pos && !Neg)   return TRI_ON_PLANE;
    else    if (Pos && Neg)     return TRI_INTERSECT;
    else    if (Pos && !Neg)    return TRI_PLUS_SPACE;
    else    if (!Pos && Neg)    return TRI_MINUS_SPACE;

    // What?!
    return TRI_FORCEDWORD;
}


/*
void Triangle::ComputeMoment(Moment& m)
{
    // Compute the area of the triangle
    m.mArea = Area();

    // Compute the centroid
    Center(m.mCentroid);

    // Second-order components. Handle zero-area faces.
    Point& p = mVerts[0];
    Point& q = mVerts[1];
    Point& r = mVerts[2];
    if(m.mArea==0.0f)
    {
        // This triangle has zero area. The second order components would be eliminated with the usual formula, so, for the 
        // sake of robustness we use an alternative form. These are the centroid and second-order components of the triangle's vertices.
        m.mCovariance.m[0][0] = (p.x*p.x + q.x*q.x + r.x*r.x);
        m.mCovariance.m[0][1] = (p.x*p.y + q.x*q.y + r.x*r.y);
        m.mCovariance.m[0][2] = (p.x*p.z + q.x*q.z + r.x*r.z);
        m.mCovariance.m[1][1] = (p.y*p.y + q.y*q.y + r.y*r.y);
        m.mCovariance.m[1][2] = (p.y*p.z + q.y*q.z + r.y*r.z);
        m.mCovariance.m[2][2] = (p.z*p.z + q.z*q.z + r.z*r.z);      
        m.mCovariance.m[2][1] = m.mCovariance.m[1][2];
        m.mCovariance.m[1][0] = m.mCovariance.m[0][1];
        m.mCovariance.m[2][0] = m.mCovariance.m[0][2];
    }
    else
    {
        const float OneOverTwelve = 1.0f / 12.0f;
        m.mCovariance.m[0][0] = m.mArea * (9.0f * m.mCentroid.x*m.mCentroid.x + p.x*p.x + q.x*q.x + r.x*r.x) * OneOverTwelve;
        m.mCovariance.m[0][1] = m.mArea * (9.0f * m.mCentroid.x*m.mCentroid.y + p.x*p.y + q.x*q.y + r.x*r.y) * OneOverTwelve;
        m.mCovariance.m[1][1] = m.mArea * (9.0f * m.mCentroid.y*m.mCentroid.y + p.y*p.y + q.y*q.y + r.y*r.y) * OneOverTwelve;
        m.mCovariance.m[0][2] = m.mArea * (9.0f * m.mCentroid.x*m.mCentroid.z + p.x*p.z + q.x*q.z + r.x*r.z) * OneOverTwelve;
        m.mCovariance.m[1][2] = m.mArea * (9.0f * m.mCentroid.y*m.mCentroid.z + p.y*p.z + q.y*q.z + r.y*r.z) * OneOverTwelve;
        m.mCovariance.m[2][2] = m.mArea * (9.0f * m.mCentroid.z*m.mCentroid.z + p.z*p.z + q.z*q.z + r.z*r.z) * OneOverTwelve;
        m.mCovariance.m[2][1] = m.mCovariance.m[1][2];
        m.mCovariance.m[1][0] = m.mCovariance.m[0][1];
        m.mCovariance.m[2][0] = m.mCovariance.m[0][2];
    }
}
*/


float Triangle::MinEdgeLength() const
{
    float Min = MAX_FLOAT;
    float Length01 = mVerts[0].Distance(mVerts[1]);
    float Length02 = mVerts[0].Distance(mVerts[2]);
    float Length12 = mVerts[1].Distance(mVerts[2]);
    if(Length01 < Min)  Min = Length01;
    if(Length02 < Min)  Min = Length02;
    if(Length12 < Min)  Min = Length12;
    return Min;
}


float Triangle::MaxEdgeLength() const
{
    float Max = MIN_FLOAT;
    float Length01 = mVerts[0].Distance(mVerts[1]);
    float Length02 = mVerts[0].Distance(mVerts[2]);
    float Length12 = mVerts[1].Distance(mVerts[2]);
    if(Length01 > Max)  Max = Length01;
    if(Length02 > Max)  Max = Length02;
    if(Length12 > Max)  Max = Length12;
    return Max;
}


void Triangle::ComputePoint(float u, float v, Point& pt, udword* nearvtx)   const
{
    // Compute point coordinates
    pt = (1.0f - u - v)*mVerts[0] + u*mVerts[1] + v*mVerts[2];

    // Compute nearest vertex if needed
    if(nearvtx)
    {
        // Compute distance vector
        Point d(mVerts[0].SquareDistance(pt),   // Distance^2 from vertex 0 to point on the face
                mVerts[1].SquareDistance(pt),   // Distance^2 from vertex 1 to point on the face
                mVerts[2].SquareDistance(pt));  // Distance^2 from vertex 2 to point on the face

        // Get smallest distance
        *nearvtx = d.SmallestAxis();
    }
}

void Triangle::Inflate(float fat_coeff, bool constant_border)
{
    // Compute triangle center
    Point TriangleCenter;
    Center(TriangleCenter);

    // Don't normalize?
    // Normalize => add a constant border, regardless of triangle size
    // Don't => add more to big triangles
    for(udword i=0;i<3;i++)
    {
        Point v = mVerts[i] - TriangleCenter;

        if(constant_border) v.Normalize();

        mVerts[i] += v * fat_coeff;
    }
}