OPC_TriBoxOverlap.h

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#define FINDMINMAX(x0, x1, x2, min, max)    \
    min = max = x0;                         \
    if(x1<min) min=x1;                      \
    if(x1>max) max=x1;                      \
    if(x2<min) min=x2;                      \
    if(x2>max) max=x2;

inline_ bool planeBoxOverlap(const Point& normal, const float d, const Point& maxbox)
{
    Point vmin, vmax;
    for(udword q=0;q<=2;q++)
    {
        if(normal[q]>0.0f)  { vmin[q]=-maxbox[q]; vmax[q]=maxbox[q]; }
        else                { vmin[q]=maxbox[q]; vmax[q]=-maxbox[q]; }
    }
    if((normal|vmin)+d>0.0f) return FALSE;
    if((normal|vmax)+d>=0.0f) return TRUE;

    return FALSE;
}

#define AXISTEST_X01(a, b, fa, fb)                          \
    min = a*v0.y - b*v0.z;                                  \
    max = a*v2.y - b*v2.z;                                  \
    if(min>max) {const float tmp=max; max=min; min=tmp; }   \
    rad = fa * extents.y + fb * extents.z;                  \
    if(min>rad || max<-rad) return FALSE;

#define AXISTEST_X2(a, b, fa, fb)                           \
    min = a*v0.y - b*v0.z;                                  \
    max = a*v1.y - b*v1.z;                                  \
    if(min>max) {const float tmp=max; max=min; min=tmp; }   \
    rad = fa * extents.y + fb * extents.z;                  \
    if(min>rad || max<-rad) return FALSE;

#define AXISTEST_Y02(a, b, fa, fb)                          \
    min = b*v0.z - a*v0.x;                                  \
    max = b*v2.z - a*v2.x;                                  \
    if(min>max) {const float tmp=max; max=min; min=tmp; }   \
    rad = fa * extents.x + fb * extents.z;                  \
    if(min>rad || max<-rad) return FALSE;

#define AXISTEST_Y1(a, b, fa, fb)                           \
    min = b*v0.z - a*v0.x;                                  \
    max = b*v1.z - a*v1.x;                                  \
    if(min>max) {const float tmp=max; max=min; min=tmp; }   \
    rad = fa * extents.x + fb * extents.z;                  \
    if(min>rad || max<-rad) return FALSE;

#define AXISTEST_Z12(a, b, fa, fb)                          \
    min = a*v1.x - b*v1.y;                                  \
    max = a*v2.x - b*v2.y;                                  \
    if(min>max) {const float tmp=max; max=min; min=tmp; }   \
    rad = fa * extents.x + fb * extents.y;                  \
    if(min>rad || max<-rad) return FALSE;

#define AXISTEST_Z0(a, b, fa, fb)                           \
    min = a*v0.x - b*v0.y;                                  \
    max = a*v1.x - b*v1.y;                                  \
    if(min>max) {const float tmp=max; max=min; min=tmp; }   \
    rad = fa * extents.x + fb * extents.y;                  \
    if(min>rad || max<-rad) return FALSE;

// compute triangle edges
// - edges lazy evaluated to take advantage of early exits
// - fabs precomputed (half less work, possible since extents are always >0)
// - customized macros to take advantage of the null component
// - axis vector discarded, possibly saves useless movs
#define IMPLEMENT_CLASS3_TESTS                      \
    float rad;                                      \
    float min, max;                                 \
                                                    \
    const float fey0 = fabsf(e0.y);                 \
    const float fez0 = fabsf(e0.z);                 \
    AXISTEST_X01(e0.z, e0.y, fez0, fey0);           \
    const float fex0 = fabsf(e0.x);                 \
    AXISTEST_Y02(e0.z, e0.x, fez0, fex0);           \
    AXISTEST_Z12(e0.y, e0.x, fey0, fex0);           \
                                                    \
    const float fey1 = fabsf(e1.y);                 \
    const float fez1 = fabsf(e1.z);                 \
    AXISTEST_X01(e1.z, e1.y, fez1, fey1);           \
    const float fex1 = fabsf(e1.x);                 \
    AXISTEST_Y02(e1.z, e1.x, fez1, fex1);           \
    AXISTEST_Z0(e1.y, e1.x, fey1, fex1);            \
                                                    \
    const Point e2 = mLeafVerts[0] - mLeafVerts[2]; \
    const float fey2 = fabsf(e2.y);                 \
    const float fez2 = fabsf(e2.z);                 \
    AXISTEST_X2(e2.z, e2.y, fez2, fey2);            \
    const float fex2 = fabsf(e2.x);                 \
    AXISTEST_Y1(e2.z, e2.x, fez2, fex2);            \
    AXISTEST_Z12(e2.y, e2.x, fey2, fex2);


inline_ bool AABBTreeCollider::TriBoxOverlap(const Point& center, const Point& extents)
{
    // Stats
    mNbBVPrimTests++;

    // use separating axis theorem to test overlap between triangle and box 
    // need to test for overlap in these directions: 
    // 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle 
    //    we do not even need to test these) 
    // 2) normal of the triangle 
    // 3) crossproduct(edge from tri, {x,y,z}-directin) 
    //    this gives 3x3=9 more tests 

    // move everything so that the boxcenter is in (0,0,0) 
    Point v0, v1, v2;
    v0.x = mLeafVerts[0].x - center.x;
    v1.x = mLeafVerts[1].x - center.x;
    v2.x = mLeafVerts[2].x - center.x;

    // First, test overlap in the {x,y,z}-directions
#ifdef OPC_USE_FCOMI
    // find min, max of the triangle in x-direction, and test for overlap in X
    if(FCMin3(v0.x, v1.x, v2.x)>extents.x)  return FALSE;
    if(FCMax3(v0.x, v1.x, v2.x)<-extents.x) return FALSE;

    // same for Y
    v0.y = mLeafVerts[0].y - center.y;
    v1.y = mLeafVerts[1].y - center.y;
    v2.y = mLeafVerts[2].y - center.y;

    if(FCMin3(v0.y, v1.y, v2.y)>extents.y)  return FALSE;
    if(FCMax3(v0.y, v1.y, v2.y)<-extents.y) return FALSE;

    // same for Z
    v0.z = mLeafVerts[0].z - center.z;
    v1.z = mLeafVerts[1].z - center.z;
    v2.z = mLeafVerts[2].z - center.z;

    if(FCMin3(v0.z, v1.z, v2.z)>extents.z)  return FALSE;
    if(FCMax3(v0.z, v1.z, v2.z)<-extents.z) return FALSE;
#else
    float min,max;
    // Find min, max of the triangle in x-direction, and test for overlap in X
    FINDMINMAX(v0.x, v1.x, v2.x, min, max);
    if(min>extents.x || max<-extents.x) return FALSE;

    // Same for Y
    v0.y = mLeafVerts[0].y - center.y;
    v1.y = mLeafVerts[1].y - center.y;
    v2.y = mLeafVerts[2].y - center.y;

    FINDMINMAX(v0.y, v1.y, v2.y, min, max);
    if(min>extents.y || max<-extents.y) return FALSE;

    // Same for Z
    v0.z = mLeafVerts[0].z - center.z;
    v1.z = mLeafVerts[1].z - center.z;
    v2.z = mLeafVerts[2].z - center.z;

    FINDMINMAX(v0.z, v1.z, v2.z, min, max);
    if(min>extents.z || max<-extents.z) return FALSE;
#endif
    // 2) Test if the box intersects the plane of the triangle
    // compute plane equation of triangle: normal*x+d=0
    // ### could be precomputed since we use the same leaf triangle several times
    const Point e0 = v1 - v0;
    const Point e1 = v2 - v1;
    const Point normal = e0 ^ e1;
    const float d = -normal|v0;
    if(!planeBoxOverlap(normal, d, extents)) return FALSE;

    // 3) "Class III" tests
    if(mFullPrimBoxTest)
    {
        IMPLEMENT_CLASS3_TESTS
    }
    return TRUE;
}

inline_ bool OBBCollider::TriBoxOverlap()
{
    // Stats
    mNbVolumePrimTests++;

    // Hook
    const Point& extents = mBoxExtents;
    const Point& v0 = mLeafVerts[0];
    const Point& v1 = mLeafVerts[1];
    const Point& v2 = mLeafVerts[2];

    // use separating axis theorem to test overlap between triangle and box 
    // need to test for overlap in these directions: 
    // 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle 
    //    we do not even need to test these) 
    // 2) normal of the triangle 
    // 3) crossproduct(edge from tri, {x,y,z}-directin) 
    //    this gives 3x3=9 more tests 

    // Box center is already in (0,0,0)

    // First, test overlap in the {x,y,z}-directions
#ifdef OPC_USE_FCOMI
    // find min, max of the triangle in x-direction, and test for overlap in X
    if(FCMin3(v0.x, v1.x, v2.x)>mBoxExtents.x)  return FALSE;
    if(FCMax3(v0.x, v1.x, v2.x)<-mBoxExtents.x) return FALSE;

    if(FCMin3(v0.y, v1.y, v2.y)>mBoxExtents.y)  return FALSE;
    if(FCMax3(v0.y, v1.y, v2.y)<-mBoxExtents.y) return FALSE;

    if(FCMin3(v0.z, v1.z, v2.z)>mBoxExtents.z)  return FALSE;
    if(FCMax3(v0.z, v1.z, v2.z)<-mBoxExtents.z) return FALSE;
#else
    float min,max;
    // Find min, max of the triangle in x-direction, and test for overlap in X
    FINDMINMAX(v0.x, v1.x, v2.x, min, max);
    if(min>mBoxExtents.x || max<-mBoxExtents.x) return FALSE;

    FINDMINMAX(v0.y, v1.y, v2.y, min, max);
    if(min>mBoxExtents.y || max<-mBoxExtents.y) return FALSE;

    FINDMINMAX(v0.z, v1.z, v2.z, min, max);
    if(min>mBoxExtents.z || max<-mBoxExtents.z) return FALSE;
#endif
    // 2) Test if the box intersects the plane of the triangle
    // compute plane equation of triangle: normal*x+d=0
    // ### could be precomputed since we use the same leaf triangle several times
    const Point e0 = v1 - v0;
    const Point e1 = v2 - v1;
    const Point normal = e0 ^ e1;
    const float d = -normal|v0;
    if(!planeBoxOverlap(normal, d, mBoxExtents)) return FALSE;

    // 3) "Class III" tests - here we always do full tests since the box is a primitive (not a BV)
    {
        IMPLEMENT_CLASS3_TESTS
    }
    return TRUE;
}

inline_ bool AABBCollider::TriBoxOverlap()
{
    // Stats
    mNbVolumePrimTests++;

    // Hook
    const Point& center     = mBox.mCenter;
    const Point& extents    = mBox.mExtents;

    // use separating axis theorem to test overlap between triangle and box 
    // need to test for overlap in these directions: 
    // 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle 
    //    we do not even need to test these) 
    // 2) normal of the triangle 
    // 3) crossproduct(edge from tri, {x,y,z}-directin) 
    //    this gives 3x3=9 more tests 

    // move everything so that the boxcenter is in (0,0,0) 
    Point v0, v1, v2;
    v0.x = mLeafVerts[0].x - center.x;
    v1.x = mLeafVerts[1].x - center.x;
    v2.x = mLeafVerts[2].x - center.x;

    // First, test overlap in the {x,y,z}-directions
#ifdef OPC_USE_FCOMI
    // find min, max of the triangle in x-direction, and test for overlap in X
    if(FCMin3(v0.x, v1.x, v2.x)>extents.x)  return FALSE;
    if(FCMax3(v0.x, v1.x, v2.x)<-extents.x) return FALSE;

    // same for Y
    v0.y = mLeafVerts[0].y - center.y;
    v1.y = mLeafVerts[1].y - center.y;
    v2.y = mLeafVerts[2].y - center.y;

    if(FCMin3(v0.y, v1.y, v2.y)>extents.y)  return FALSE;
    if(FCMax3(v0.y, v1.y, v2.y)<-extents.y) return FALSE;

    // same for Z
    v0.z = mLeafVerts[0].z - center.z;
    v1.z = mLeafVerts[1].z - center.z;
    v2.z = mLeafVerts[2].z - center.z;

    if(FCMin3(v0.z, v1.z, v2.z)>extents.z)  return FALSE;
    if(FCMax3(v0.z, v1.z, v2.z)<-extents.z) return FALSE;
#else
    float min,max;
    // Find min, max of the triangle in x-direction, and test for overlap in X
    FINDMINMAX(v0.x, v1.x, v2.x, min, max);
    if(min>extents.x || max<-extents.x) return FALSE;

    // Same for Y
    v0.y = mLeafVerts[0].y - center.y;
    v1.y = mLeafVerts[1].y - center.y;
    v2.y = mLeafVerts[2].y - center.y;

    FINDMINMAX(v0.y, v1.y, v2.y, min, max);
    if(min>extents.y || max<-extents.y) return FALSE;

    // Same for Z
    v0.z = mLeafVerts[0].z - center.z;
    v1.z = mLeafVerts[1].z - center.z;
    v2.z = mLeafVerts[2].z - center.z;

    FINDMINMAX(v0.z, v1.z, v2.z, min, max);
    if(min>extents.z || max<-extents.z) return FALSE;
#endif
    // 2) Test if the box intersects the plane of the triangle
    // compute plane equation of triangle: normal*x+d=0
    // ### could be precomputed since we use the same leaf triangle several times
    const Point e0 = v1 - v0;
    const Point e1 = v2 - v1;
    const Point normal = e0 ^ e1;
    const float d = -normal|v0;
    if(!planeBoxOverlap(normal, d, extents)) return FALSE;

    // 3) "Class III" tests - here we always do full tests since the box is a primitive (not a BV)
    {
        IMPLEMENT_CLASS3_TESTS
    }
    return TRUE;
}