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TriangleIntersectAABB

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hi, anybody knows a functions to check if that is true. (maybe also a function to check it its fully inside ;) ) Triangle defined by v1,v2,v3 which are x/y/z floats. AABB definded by MinPt, MaxPt which are x/y/z floats. thank you

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1. test if bounding box of a triangle and your box overlap. if they don't return false
2. test if plane of your triangle intersects box. if it doesn't return false
3. perform 3 2d tests
for each coordinate system plane
test if projection of box (rectangle) overlaps projection of a triangle
if at least one such test reports non overlap - return false
return true
this method is actually test using minkowski sum, just simplified.

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I'd recommend you use the SAT.



void getTriangleInterval(const Vector& axis, const Vector& v1, const Vector& v2, const Vector& v3, float& min, float& max)
{
float d1 = v1.dotProduct(axis);
float d2 = v2.dotProduct(axis);
float d3 = v3.dotProduct(axis);

min = max = d1;
if(d2 < min) min = d2; else if (d2 > max) max = d2;
if(d3 < min) min = d3; else if (d3 > max) max = d3;
}

void getAABBInterval(const Vector& axis, const Vector& aabbmin, const Vector& aabbmax, float& min, float& max)
{
Vector centre = (aabbmax + aabbmin) * 0.5f;
Vector halfsize = (aabbmax - aabbmin) * 0.5f;
float p = centre.dotProduct(axis);
float rx = fabs(axis.x) * halfsize.x;
float ry = fabs(axis.y) * halfsize.y;
float rz = fabs(axis.z) * halfsize.z;
float r = rx + ry + rz;

min = p - r;
max = p + r;
}

bool triangleAABBSeparated(const Vector& axis, const Vector& v1, const Vector& v2, const Vector& v3, const Vector& min, const Vector& max)
{
// degenerate case
float axisLengthSquared = axis.dotProduct(axis);
if(axisLengthSquared < 1.0E-8f)
return false;

// the box interval
float aabbmin, aabbmax;
getAABBInterval(axis, min, max, aabbmin, aabbmax);

// the triangle interval
float trimin, trimax;
getTriangleInterval(axis, v1, v2, v3, trimin, trimax);

// check for interval overlap
if(trimin > aabmax || aabbmin > trimax)
return true;
else
return false;
}

bool triangleAABBIntersect(const Vector& v1, const Vector& v2, const Vector& v3, const Vector& min, const Vector& max)
{
// the separation axis to test
Vector axis;

// triangle plane
axis = (v2 - v1).crossProduct(v3 - v2);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

// box axes
axis = Vector(1, 0, 0);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(0, 1, 0);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(0, 0, 1);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

// first cross axes
axis = Vector(1, 0, 0).crossProduct(v2 - v1);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(1, 0, 0).crossProduct(v3 - v2);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(1, 0, 0).crossProduct(v1 - v3);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

// second cross axes
axis = Vector(0, 1, 0).crossProduct(v2 - v1);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(0, 1, 0).crossProduct(v3 - v2);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(0, 1, 0).crossProduct(v1 - v3);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

// third cross axes
axis = Vector(0, 0, 1).crossProduct(v2 - v1);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(0, 0, 1).crossProduct(v3 - v2);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

axis = Vector(0, 0, 1).crossProduct(v1 - v3);
if(triangleAABBSeparated(axis, v1, v2, v3, min, max)) return false;

return true;
}

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for containment, after the intersection is positive, check if the three corners are inside the box.

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