Float-vectors

A float-vector is a simple vector whose elements are specialized to floating point numbers. A float-vector can be of any size. When result is specified in an argument list, it should be a float-vector that holds the result.

float-vector &rest numbers [function]

makes a new float-vector whose elements are numbers. Note the difference between (float-vector 1 2 3) and #F(1 2 3). While the former create a vector each time it is called, the latter does when it is read.

float-vector-p obj [function]

returns T if obj is a float-vector.

v+ fltvec1 fltvec2 &optional result [function]

adds two float-vectors.

v- fltvec1 &optional fltvec2 result [function]

subtract float-vectors. If fltvec2 is omitted, fltvec1 is negated.

v. fltvec1 fltvec2 [function]

computes the inner product of two float-vectors.

v* fltvec1 fltvec2 &optional result [function]

computes the outer product of two float-vectors.

v.* fltvec1 fltvec2 fltvec3 [function]

computes the scaler triple product [A,B,C]=(V. A (V* B C))=(V. (V* A B) C).

v$<$ fltvec1 fltvec2 [function]

returns T if every element of fltvec1 is smaller than the corresponding element of fltvec2.

v$>$ fltvec1 fltvec2 [function]

returns T if every element of fltvec1 is larger than the corresponding element of fltvec2.

vmin &rest fltvec [function]

finds the smallest values for each dimension in fltvec, and makes a float-vector from the values. Vmin and vmax are used to find the minimal bounding box from coordinates of vertices.

vmax &rest fltvec [function]

finds the greatest values for each dimension in fltvec, and makes a float-vector from the values.

minimal-box v-list minvec maxvec [err] [function]

computes the minimal bounding box for a given vertex-list, and stores results in minvec and maxvec. If a floating number err is specified, the minimal box is grown by the ratio, i.e. if the err is 0.01, each element of minvec is decreased by 1% of the distance between minvec and maxvec, and each element of maxvec is increased by 1%. Minimal-box returns the distance between minvec and maxvec.

scale number fltvec &optional result [function]

the scaler number is multiplied to the every element of fltvec.

norm fltvec [function]

$\vert fltvec\vert$

norm2 fltvec [function]

$\vert fltvec\vert^2=({\bf v.} fltvec fltvec)$

normalize-vector fltvec [result] [function]

normalizes fltvec to have the norm 1.0.

distance fltvec1 fltvec2 [function]

returns the distance $\vert fltvec-fltvec2\vert$ between two float-vectors.

distance2 fltvec1 fltvec2 [function]

$\vert fltvec-fltvec2\vert^2$

homo2normal homovec &optional normalvec [function]

A homogeneous vector homovec is converted to its normal representation.

homogenize normalvec &optional homovec [function]

A normal vector normalvec is converted to its homogenous representation.

midpoint p p1 p2 &optional result [function]

P is float, and p1 and p2 are float-vectors of the same dimension. A point $(1-p) p1 + p p2$, which is the point that breaks p1-p2 by the ratio $p:(1-p)$, is returned.

rotate-vector fltvec theta axis &optional result [function]

rotates 2D or 3D fltvec by theta radian around axis. Axis can be one of :x, :y, :z, 0, 1, 2 or NIL. When axis is NIL, fltvec is taken to be two dimensional. To rotate a vector around an arbitrary axis in 3D space, make a rotation matrix by the rotation-matrix function and multiply it to the vector.