IceIndexedTriangle.cpp

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// Precompiled Header
#include "Stdafx.h"


using namespace Opcode;




void IndexedTriangle::Flip()
{
    Swap(mVRef[1], mVRef[2]);
}


float IndexedTriangle::Area(const Point* verts) const
{
    if(!verts)  return 0.0f;
    const Point& p0 = verts[0];
    const Point& p1 = verts[1];
    const Point& p2 = verts[2];
    return ((p0-p1)^(p0-p2)).Magnitude() * 0.5f;
}


float IndexedTriangle::Perimeter(const Point* verts)    const
{
    if(!verts)  return 0.0f;
    const Point& p0 = verts[0];
    const Point& p1 = verts[1];
    const Point& p2 = verts[2];
    return      p0.Distance(p1)
            +   p0.Distance(p2)
            +   p1.Distance(p2);
}


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


void IndexedTriangle::Normal(const Point* verts, Point& normal) const
{
    if(!verts)  return;

    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];
    normal = ((p2-p1)^(p0-p1)).Normalize();
}


void IndexedTriangle::DenormalizedNormal(const Point* verts, Point& normal) const
{
    if(!verts)  return;

    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];
    normal = ((p2-p1)^(p0-p1));
}


void IndexedTriangle::Center(const Point* verts, Point& center) const
{
    if(!verts)  return;

    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];
    center = (p0+p1+p2)*INV3;
}


void IndexedTriangle::CenteredNormal(const Point* verts, Point& normal) const
{
    if(!verts)  return;

    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];
    Point Center = (p0+p1+p2)*INV3;
    normal = Center + ((p2-p1)^(p0-p1)).Normalize();
}


void IndexedTriangle::RandomPoint(const Point* verts, Point& random)    const
{
    if(!verts)  return;

    // Random barycentric coords
    float Alpha = UnitRandomFloat();
    float Beta  = UnitRandomFloat();
    float Gamma = UnitRandomFloat();
    float OneOverTotal = 1.0f / (Alpha + Beta + Gamma);
    Alpha   *= OneOverTotal;
    Beta    *= OneOverTotal;
    Gamma   *= OneOverTotal;

    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];
    random = Alpha*p0 + Beta*p1 + Gamma*p2;
}


bool IndexedTriangle::IsVisible(const Point* verts, const Point& source)    const
{
    // Checkings
    if(!verts)  return false;

    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];

    // Compute denormalized normal
    Point Normal = (p2 - p1)^(p0 - p1);

    // Backface culling
    return (Normal | source) >= 0.0f;

// Same as:
//  Plane PL(verts[mVRef[0]], verts[mVRef[1]], verts[mVRef[2]]);
//  return PL.Distance(source) > PL.d;
}


bool IndexedTriangle::BackfaceCulling(const Point* verts, const Point& source)  const
{
    // Checkings
    if(!verts)  return false;

    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];

    // Compute base
//  Point Base = (p0 + p1 + p2)*INV3;

    // Compute denormalized normal
    Point Normal = (p2 - p1)^(p0 - p1);

    // Backface culling
//  return (Normal | (source - Base)) >= 0.0f;
    return (Normal | (source - p0)) >= 0.0f;

// Same as: (but a bit faster)
//  Plane PL(verts[mVRef[0]], verts[mVRef[1]], verts[mVRef[2]]);
//  return PL.Distance(source)>0.0f;
}


float IndexedTriangle::ComputeOcclusionPotential(const Point* verts, const Point& view) const
{
    if(!verts)  return 0.0f;
    // Occlusion potential: -(A * (N|V) / d^2)
    // A = polygon area
    // N = polygon normal
    // V = view vector
    // d = distance viewpoint-center of polygon

    float A = Area(verts);
    Point N;    Normal(verts, N);
    Point C;    Center(verts, C);
    float d = view.Distance(C);
    return -(A*(N|view))/(d*d);
}


bool IndexedTriangle::ReplaceVertex(udword oldref, udword newref)
{
            if(mVRef[0]==oldref)    { mVRef[0] = newref; return true; }
    else    if(mVRef[1]==oldref)    { mVRef[1] = newref; return true; }
    else    if(mVRef[2]==oldref)    { mVRef[2] = newref; return true; }
    return false;
}


bool IndexedTriangle::IsDegenerate()    const
{
    if(mVRef[0]==mVRef[1])  return true;
    if(mVRef[1]==mVRef[2])  return true;
    if(mVRef[2]==mVRef[0])  return true;
    return false;
}


bool IndexedTriangle::HasVertex(udword ref) const
{
    if(mVRef[0]==ref)   return true;
    if(mVRef[1]==ref)   return true;
    if(mVRef[2]==ref)   return true;
    return false;
}


bool IndexedTriangle::HasVertex(udword ref, udword* index)  const
{
    if(mVRef[0]==ref)   { *index = 0;   return true; }
    if(mVRef[1]==ref)   { *index = 1;   return true; }
    if(mVRef[2]==ref)   { *index = 2;   return true; }
    return false;
}


ubyte IndexedTriangle::FindEdge(udword vref0, udword vref1) const
{
            if(mVRef[0]==vref0 && mVRef[1]==vref1)  return 0;
    else    if(mVRef[0]==vref1 && mVRef[1]==vref0)  return 0;
    else    if(mVRef[0]==vref0 && mVRef[2]==vref1)  return 1;
    else    if(mVRef[0]==vref1 && mVRef[2]==vref0)  return 1;
    else    if(mVRef[1]==vref0 && mVRef[2]==vref1)  return 2;
    else    if(mVRef[1]==vref1 && mVRef[2]==vref0)  return 2;
    return 0xff;
}


udword IndexedTriangle::OppositeVertex(udword vref0, udword vref1)  const
{
            if(mVRef[0]==vref0 && mVRef[1]==vref1)  return mVRef[2];
    else    if(mVRef[0]==vref1 && mVRef[1]==vref0)  return mVRef[2];
    else    if(mVRef[0]==vref0 && mVRef[2]==vref1)  return mVRef[1];
    else    if(mVRef[0]==vref1 && mVRef[2]==vref0)  return mVRef[1];
    else    if(mVRef[1]==vref0 && mVRef[2]==vref1)  return mVRef[0];
    else    if(mVRef[1]==vref1 && mVRef[2]==vref0)  return mVRef[0];
    return INVALID_ID;
}


void IndexedTriangle::GetVRefs(ubyte edgenb, udword& vref0, udword& vref1, udword& vref2) const
{
    if(edgenb==0)
    {
        vref0 = mVRef[0];
        vref1 = mVRef[1];
        vref2 = mVRef[2];
    }
    else if(edgenb==1)
    {
        vref0 = mVRef[0];
        vref1 = mVRef[2];
        vref2 = mVRef[1];
    }
    else if(edgenb==2)
    {
        vref0 = mVRef[1];
        vref1 = mVRef[2];
        vref2 = mVRef[0];
    }
}


float IndexedTriangle::MinEdgeLength(const Point* verts)    const
{
    if(!verts)  return 0.0f;

    float Min = MAX_FLOAT;
    float Length01 = verts[0].Distance(verts[1]);
    float Length02 = verts[0].Distance(verts[2]);
    float Length12 = verts[1].Distance(verts[2]);
    if(Length01 < Min)  Min = Length01;
    if(Length02 < Min)  Min = Length02;
    if(Length12 < Min)  Min = Length12;
    return Min;
}


float IndexedTriangle::MaxEdgeLength(const Point* verts)    const
{
    if(!verts)  return 0.0f;

    float Max = MIN_FLOAT;
    float Length01 = verts[0].Distance(verts[1]);
    float Length02 = verts[0].Distance(verts[2]);
    float Length12 = verts[1].Distance(verts[2]);
    if(Length01 > Max)  Max = Length01;
    if(Length02 > Max)  Max = Length02;
    if(Length12 > Max)  Max = Length12;
    return Max;
}


void IndexedTriangle::ComputePoint(const Point* verts, float u, float v, Point& pt, udword* nearvtx)    const
{
    // Checkings
    if(!verts)  return;

    // Get face in local or global space
    const Point& p0 = verts[mVRef[0]];
    const Point& p1 = verts[mVRef[1]];
    const Point& p2 = verts[mVRef[2]];

    // Compute point coordinates
    pt = (1.0f - u - v)*p0 + u*p1 + v*p2;

    // Compute nearest vertex if needed
    if(nearvtx)
    {
        // Compute distance vector
        Point d(p0.SquareDistance(pt),  // Distance^2 from vertex 0 to point on the face
                p1.SquareDistance(pt),  // Distance^2 from vertex 1 to point on the face
                p2.SquareDistance(pt)); // Distance^2 from vertex 2 to point on the face

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

    //**************************************
    // Angle between two vectors (in radians)
    // we use this formula
    // uv = |u||v| cos(u,v)
    // u  ^ v  = w
    // |w| = |u||v| |sin(u,v)|
    //**************************************
    float Angle(const Point& u, const Point& v)
    {
        float NormU = u.Magnitude();    // |u|
        float NormV = v.Magnitude();    // |v|
        float Product = NormU*NormV;    // |u||v|
        if(Product==0.0f)   return 0.0f;
        float OneOverProduct = 1.0f / Product;

        // Cosinus
        float Cosinus = (u|v) * OneOverProduct;

        // Sinus
        Point w = u^v;
        float NormW = w.Magnitude();

        float AbsSinus = NormW * OneOverProduct;

        // Remove degeneracy
        if(AbsSinus > 1.0f) AbsSinus = 1.0f;
        if(AbsSinus < -1.0f) AbsSinus = -1.0f;

        if(Cosinus>=0.0f)   return asinf(AbsSinus);
        else                return (PI-asinf(AbsSinus));
    }


float IndexedTriangle::Angle(const IndexedTriangle& tri, const Point* verts)    const
{
    // Checkings
    if(!verts)  return 0.0f;

    // Compute face normals
    Point n0, n1;
    Normal(verts, n0);
    tri.Normal(verts, n1);

    // Compute angle
    float dp = n0|n1;
    if(dp>1.0f)     return 0.0f;
    if(dp<-1.0f)    return PI;
    return acosf(dp);

//  return ::Angle(n0,n1);
}


bool IndexedTriangle::Equal(const IndexedTriangle& tri) const
{
    // Test all vertex references
    return (HasVertex(tri.mVRef[0]) && 
            HasVertex(tri.mVRef[1]) &&
            HasVertex(tri.mVRef[2]));
}