Principle Component Analysis (PCA)

Collaboration diagram for Principle Component Analysis (PCA):

Functions
int	bg_pca (point_t *c, vect_t *xaxis, vect_t *yaxis, vect_t *zaxis, size_t npnts, point_t *pnts)
	Perform a Principle Component Analysis on a set of points.

Detailed Description

Principle Component Analysis

Calculates an XYZ coordinate system such that it aligns with the largest variations in the supplied data. Intuitively, it "aligns" with the shape of the points.

To apply the coordinate system to the input points to relocate them to the aligned position in model space, you can construct matrices and apply them:

point_t center;
vect_t xaxis, yaxis, zaxis;
bg_pca(&center, &xaxis, &yaxis, &zaxis, pntcnt, pnts);
mat_t R, T, RT;
// Rotation
MAT_IDN(R);
VMOVE(&R[0], xaxis);
VMOVE(&R[4], yaxis);
VMOVE(&R[8], zaxis);
// Translation
MAT_IDN(T);
MAT_DELTAS_VEC_NEG(T, center);
// Combine
bn_mat_mul(RT, R, T);
// Apply
point_t p;
for (size_t i = 0; i < pntcnt; i++) {
    MAT4X3PNT(p, RT, pnts[i]);
    VMOVE(pnts[i], v);
}

Function Documentation

bg_pca()

int bg_pca ( point_t *  c, vect_t *  xaxis, vect_t *  yaxis, vect_t *  zaxis, size_t  npnts, point_t *  pnts  )

extern

Perform a Principle Component Analysis on a set of points.

Outputs are a center point and XYZ vectors for the coordinate system.

Parameters

[out]	c	Origin of aligned coordinate system
[out]	xaxis	Vector of X axis of aligned coordinate system (unit length)
[out]	yaxis	Vector of Y axis of aligned coordinate system (unit length)
[out]	zaxis	Vector of Z axis of aligned coordinate system (unit length)
[in]	npnts	Number of points in input pnts array
[in]	pnts	Array of points to analyze

Returns

BRLCAD_OK success

BRLCAD_ERROR if inputs are invalid or calculation fails