public bool IntersectsPrincipalRectangle(
PrincipalSpace3D principalSpace3D,
PrincipalTrajectory principalTrajectory,
Vector2 principalTargetPosition,
Matrix4x4 localToWorldMatrix,
Vector3 boundsCenter,
Vector3 boundsExtents,
float marginDistance,
ref Matrix4x4 localToPrincipalMatrix)
{
_localToWorldMatrix = localToWorldMatrix;
Vector3 axisZ = Vector3.Cross(principalSpace3D.xAxis, principalSpace3D.yAxis);
// Get the non-uniform scale of the matrix based on the bounding box size
// and marginDistance
Vector3 scale = GetMarginMatrixScale(boundsExtents, marginDistance);
// Get the data necessary to get the z component in principal space
// of any local vertex (not considering translation yet).
localToPrincipalMatrix.m20 = DotMatrixColumn0(axisZ) * scale.x;
localToPrincipalMatrix.m21 = DotMatrixColumn1(axisZ) * scale.y;
localToPrincipalMatrix.m22 = DotMatrixColumn2(axisZ) * scale.z;
Vector3 relBoundsCenter = _localToWorldMatrix.MultiplyPoint(boundsCenter) - principalSpace3D.p0;
float principalBoundsCenterZ = Vector3.Dot(relBoundsCenter, axisZ);
// Get the bounding box size projected onto the principal z axis
float extentsZ = Mathf.Abs(localToPrincipalMatrix.m20) * boundsExtents.x +
Mathf.Abs(localToPrincipalMatrix.m21) * boundsExtents.y +
Mathf.Abs(localToPrincipalMatrix.m22) * boundsExtents.z;
if (Mathf.Abs(principalBoundsCenterZ) > extentsZ)
{
return(false); // bounding box doens't intersect the principal plane
}
// Get the data necessary to get the x component in principal space
// of any local vertex (not considering translation yet).
localToPrincipalMatrix.m00 = DotMatrixColumn0(principalSpace3D.xAxis) * scale.x;
localToPrincipalMatrix.m01 = DotMatrixColumn1(principalSpace3D.xAxis) * scale.y;
localToPrincipalMatrix.m02 = DotMatrixColumn2(principalSpace3D.xAxis) * scale.z;
// Test the bounding box projected on the x axis of the principal space
// against the initial (i.e. min) and target (i.e. max) x interval.
float principalBoundsCenterX = Vector3.Dot(relBoundsCenter, principalSpace3D.xAxis);
float extentsX = Mathf.Abs(localToPrincipalMatrix.m00) * boundsExtents.x +
Mathf.Abs(localToPrincipalMatrix.m01) * boundsExtents.y +
Mathf.Abs(localToPrincipalMatrix.m02) * boundsExtents.z;
if (principalBoundsCenterX + extentsX < 0 ||
principalBoundsCenterX - extentsX > principalTargetPosition.x)
{
return(false);
}
// Get the data necessary to get the y component in principal space
// of any local vertex (not considering translation yet).
localToPrincipalMatrix.m10 = DotMatrixColumn0(principalSpace3D.yAxis) * scale.x;
localToPrincipalMatrix.m11 = DotMatrixColumn1(principalSpace3D.yAxis) * scale.y;
localToPrincipalMatrix.m12 = DotMatrixColumn2(principalSpace3D.yAxis) * scale.z;
// Test the bounding box projected on the y axis of the principal space
// against the min and max y interval.
float principalBoundsCenterY = Vector3.Dot(relBoundsCenter, principalSpace3D.yAxis);
float extentsY = Mathf.Abs(localToPrincipalMatrix.m10) * boundsExtents.x +
Mathf.Abs(localToPrincipalMatrix.m11) * boundsExtents.y +
Mathf.Abs(localToPrincipalMatrix.m12) * boundsExtents.z;
if (principalBoundsCenterY + extentsY < Mathf.Min(0.0f, principalTargetPosition.y) ||
principalBoundsCenterY - extentsY > principalTrajectory.PositionAtTime(
principalTrajectory.GetTimeAtMaximumHeight()).y)
{
return(false);
}
// Get the data necessary to do the translation part from local to
// principal space
Vector3 delta = new Vector3(_localToWorldMatrix.m03 - principalSpace3D.p0.x,
_localToWorldMatrix.m13 - principalSpace3D.p0.y,
_localToWorldMatrix.m23 - principalSpace3D.p0.z);
localToPrincipalMatrix.m03 = Vector3.Dot(delta, principalSpace3D.xAxis);
localToPrincipalMatrix.m13 = Vector3.Dot(delta, principalSpace3D.yAxis);
localToPrincipalMatrix.m23 = Vector3.Dot(delta, axisZ);
// No projection components
localToPrincipalMatrix.m30 = 0;
localToPrincipalMatrix.m31 = 0;
localToPrincipalMatrix.m32 = 0;
localToPrincipalMatrix.m33 = 1;
return(true);
}
