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