Separating Axis Test for Axis-Aligned Bounding Box and Triangle produces incorrect results (3D)

Question

I\'m doing triangle to AABB intersection tests, and I\'m taking this sample code from Real-Time Collision Detection by Christer Ericson. What the author says in the boo

Answer 1

The reason that I was getting false positives for my tests was related to the triangle test.

To test a triangle, which is a plane in 3D space, you have to test against 4 axes(aka normals).

1. Surface Normal
   
   • The cross-product between two edges of the triangle.
2. Edge Normal 1
   
   • The cross product between the surface normal and edge 1.
3. Edge Normal 2
   
   • The cross product between the surface normal and edge 2.
4. Edge Normal 3
   
   • The cross product between the surface normal and edge 3.

So in the end, to get a proper (at least it is working correctly so far) collision test between a cube and a triangle, you have to perform 7 axes tests.

Each test consists of checking the triangle and box vertices against the axis (normal). This can be broken down into a triangle and box test, and if one has a separating axis, then you don't have to do the other.

Note: This test will only give you true/false results. No other data is provided.

public static boolean testTriangleAABB( Triangle triangle, 
        Vector3d origin, double size ) {
    setTriangleNormal( triangle.getNormal( true ) );
    Vector3d[] aabbVertices = calculateAABBVertices( origin, size );

    // Triangle Normal axis test, false = No Collision.
    if( !testTriangleNormal( triangle, aabbVertices ) ) {
        return false;
    }

    // Triangle Edge Normals axis test, false = No Collision.
    if( !testTriangleEdgeNormals( triangle, aabbVertices ) ) {
        return false;
    }

    // Axis-Aligned Bounding Box X, Y, Z axis test, false = No Collision.
    if( !testAABBAxis( triangle, aabbVertices ) ) {
        return false;
    }     

    // if we get here then we know that every axis had overlap on it
    // so we can guarantee an intersection
    return true;
}

...

private static boolean testTriangleEdgeNormals( Triangle triangle, Vector3d[] aabbVertices ) {
    Vector3d edge = new Vector3d();
    Vector3d edgeNormal = new Vector3d();

    // loop over the triangle edge normals
    Vector3d[] points = triangle.getPoints();
    for( int i = 0; i < points.length; i++ ) {
        int iOverflow = i + 1 == points.length ? 0 : i + 1;
        edge.sub( points[ i ], points[ iOverflow ] );
        edge.normalize();
        edgeNormal.cross( getTriangleNormal(), edge );

        // project both shapes onto the axis
        projectionAABB = project2D1D( aabbVertices, edgeNormal );
        projectionTriangle = project2D1D( triangle.getPoints(), edgeNormal );
        // do the projections overlap?
        if ( !projectionAABB.hasOverlap( projectionTriangle ) ) {
            // then we can guarantee that the shapes do not overlap
            return false;
        }
    }
    return true;
}

Furthermore, there is no need to calculate Axis-Aligned Bounding Box axes..since they are axis aligned the axes will be like so:

private static final Vector3d[] AABB_AXES = { 
    new Vector3d( -1.0, 0.0, 0.0 ), 
    new Vector3d( 0.0, -1.0, 0.0 ),
    new Vector3d( 0.0, 0.0, -1.0 ) };

Answer 2

You can check my c# (almost identical to java in this case...) implantation in a game i made a little while ago. http://code.google.com/p/gotcha/source/browse/trunk/Gotcha/trunk/Gotcha/Gotcha/GameEnteties/GameEntity.cs#171

Look for the method : IsSATCollision

Think about the parameter it accepts as just something that has vertices for simplicity.