Linear Algebra

Linear algebra transformations on Euclidean coordinates. More...

Collaboration diagram for Linear Algebra:

Files
file	math-base.scad
	Include file wrapper of math base primitives.

Functions
function	multmatrix_lp (c, m)
	Multiply all coordinates by a 4x4 3d-transformation matrix. More...
function	translate_lp (c, v)
	Translate all coordinates dimensions. More...
function	rotate_lp (c, a, v, o=origin3d)
	Rotate all coordinates about one or more axes in Euclidean 2d or 3d space. More...
function	scale_lp (c, v)
	Scale all coordinates dimensions. More...
function	resize_lp (c, v)
	Scale all coordinates dimensions proportionately to fit inside a region. More...

Detailed Description

Linear algebra transformations on Euclidean coordinates.

Function Documentation

function multmatrix_lp	(	c	,
		m
	)

Multiply all coordinates by a 4x4 3d-transformation matrix.

Parameters

c	<coords-3d> A list of 3d coordinate points.
m	<matrix-4x4> A 4x4 transformation matrix (decimal-list-4-list4).

Returns

<coords-3d> A list of 3d coordinate points multiplied by the transformation matrix.

See Wikipedia and multmatrix for more information.

function resize_lp	(	c	,
		v
	)

Scale all coordinates dimensions proportionately to fit inside a region.

Parameters

c	<coords-nd> A list of nd coordinate points.
v	<decimal-list-n> A list of bounds for each dimension.

Returns

<coords-nd> A list of proportionately scaled coordinate points which exactly fit the region bounds v.

function rotate_lp	(	c	,
		a	,
		v	,
		o	= origin3d
	)

Rotate all coordinates about one or more axes in Euclidean 2d or 3d space.

Parameters

c	<coords-3d|coords-2d> A list of 3d or 2d coordinate points.
a	<decimal-list-3|decimal> The axis rotation angle. A list [ax, ay, az] or a single decimal to specify az only.
v	<vector-3d> An arbitrary axis for the rotation. When specified, the rotation angle will be a or az about the line v that passes through point o.
o	<point-3d> A 3d point origin for the rotation. Ignored when v is not specified.

Returns

<coords-3d|coords-2d> A list of 3d or 2d rotated coordinates. Rotation order is rz, ry, rx.

See Wikipedia for more information on transformation matrix and axis rotation.

function scale_lp	(	c	,
		v
	)

Scale all coordinates dimensions.

Parameters

c	<coords-nd> A list of nd coordinate points.
v	<decimal-list-n> A list of scalers for each dimension.

Returns

<coords-nd> A list of scaled coordinate points.

function translate_lp	(	c	,
		v
	)

Translate all coordinates dimensions.

Parameters

c	<coords-nd> A list of nd coordinate points.
v	<decimal-list-n> A list of translations for each dimension.

Returns

<coords-nd> A list of translated coordinate points.

See Wikipedia for more information and transformation matrix.