BOSL2/vectors.scad
2019-04-22 20:55:03 -07:00

115 lines
3.7 KiB
OpenSCAD

//////////////////////////////////////////////////////////////////////
// LibFile: vectors.scad
// Vector math functions.
// To use, add the following lines to the beginning of your file:
// ```
// use <BOSL2/std.scad>
// ```
//////////////////////////////////////////////////////////////////////
/*
BSD 2-Clause License
Copyright (c) 2017-2019, Revar Desmera
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
// Section: Vector Manipulation
// Function: vmul()
// Description:
// Element-wise vector multiplication. Multiplies each element of vector `v1` by
// the corresponding element of vector `v2`. Returns a vector of the products.
// Arguments:
// v1 = The first vector.
// v2 = The second vector.
// Example:
// vmul([3,4,5], [8,7,6]); // Returns [24, 28, 30]
function vmul(v1, v2) = [for (i = [0:len(v1)-1]) v1[i]*v2[i]];
// Function: vdiv()
// Description:
// Element-wise vector division. Divides each element of vector `v1` by
// the corresponding element of vector `v2`. Returns a vector of the quotients.
// Arguments:
// v1 = The first vector.
// v2 = The second vector.
// Example:
// vdiv([24,28,30], [8,7,6]); // Returns [3, 4, 5]
function vdiv(v1, v2) = [for (i = [0:len(v1)-1]) v1[i]/v2[i]];
// Function: vabs()
// Description: Returns a vector of the absolute value of each element of vector `v`.
// Arguments:
// v = The vector to get the absolute values of.
function vabs(v) = [for (x=v) abs(x)];
// Function: normalize()
// Description:
// Returns unit length normalized version of vector v.
// Arguments:
// v = The vector to normalize.
function normalize(v) = v/norm(v);
// Function: vector_angle()
// Usage:
// vector_angle(v1,v2);
// Description:
// Returns angle in degrees between two vectors of similar dimensions.
// Arguments:
// v1 = First vector.
// v2 = Second vector.
// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
function vector_angle(v1,v2) =
assert(is_vector(v1))
assert(is_vector(v2))
acos(constrain((v1*v2)/(norm(v1)*norm(v2)), -1, 1));
// Function: vector_axis()
// Usage:
// vector_xis(v1,v2);
// Description:
// Returns the vector perpendicular to both of the given vectors.
// Arguments:
// v1 = First vector.
// v2 = Second vector.
function vector_axis(v1,v2) =
let(
eps = 1e-6,
v1 = point3d(v1/norm(v1)),
v2 = point3d(v2/norm(v2)),
v3 = (norm(v1-v2) > eps && norm(v1+v2) > eps)? v2 :
(norm(vabs(v2)-UP) > eps)? UP :
RIGHT
) normalize(cross(v1,v3));
// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap