GPGPU Programming for Games and Science

Linear and Affine Algebra 267

template <typename Real>

Re al ComputeOrthogonalComplement ( int numInputs , Vector3<Real>∗ v);

LISTING 6.11: The 3D vector interface for computing orthogonal comple-

ments.

The return values of the functions is the minimum length of the unnormalized

vectors constructed during the Gram-Schmidt algorithm. It is possible the

inputs are nearly linearly dependent, in a numerical sense, in which case the

return value is nearly zero. The function provides a consistent signature across

dimensions. The

numInputs must be one or two and v[] must have numInputs

vectors.

6.1.3.3 Orthonormal Sets in 4D

This section shows how the concepts in three dimensions extend to four

dimensions.

One Vector from Three Inputs. Consider three vectors V