IceTriangle.cpp

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// Precompiled Header
#include "Stdafx.h"

using namespace IceMaths;




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;
        }
}