mirror of
https://github.com/BelfrySCAD/BOSL2.git
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190 lines
7.5 KiB
OpenSCAD
190 lines
7.5 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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// Section: Vector Manipulation
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// Function: is_vector()
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// Usage:
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// is_vector(v, [length], [fast]);
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// Description:
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// Returns true if v is a list of finite numbers.
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// Arguments:
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// v = The value to test to see if it is a vector.
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// length = If given, make sure the vector is `length` items long.
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// fast = If true, do a shallow test that is faster.
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// Example:
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// is_vector(4); // Returns false
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// is_vector([4,true,false]); // Returns false
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// is_vector([3,4,INF,5]); // Returns false
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// is_vector([3,4,5,6]); // Returns true
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// is_vector([3,4,undef,5]); // Returns false
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// is_vector([3,4,5],3); // Returns true
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// is_vector([3,4,5],4); // Returns true
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// is_vector([]); // Returns false
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// is_vector([3,undef,undef,true], fast=true); // Returns true
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function is_vector(v,length,fast=false) =
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(fast? (is_list(v) && is_num(v[0])) : is_list_of(v,0)) &&
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len(v) && (is_undef(length) || length==len(v));
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// Function: add_scalar()
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// Usage:
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// add_scalar(v,s);
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// Description:
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// Given a vector and a scalar, returns the vector with the scalar added to each item in it.
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// If given a list of vectors, recursively adds the scalar to the each vector.
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// Arguments:
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// v = The initial list of values.
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// s = A scalar value to add to every item in the vector.
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// Example:
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// add_scalar([1,2,3],3); // Returns: [4,5,6]
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// add_scalar([[1,2,3],[3,4,5]],3); // Returns: [[4,5,6],[6,7,8]]
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function add_scalar(v,s) = [for (x=v) is_list(x)? add_scalar(x,s) : x+s];
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// Function: vang()
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// Usage:
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// theta = vang([X,Y]);
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// theta_phi = vang([X,Y,Z]);
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// Description:
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// Given a 2D vector, returns the angle in degrees counter-clockwise from X+ on the XY plane.
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// Given a 3D vector, returns [THETA,PHI] where THETA is the number of degrees counter-clockwise from X+ on the XY plane, and PHI is the number of degrees up from the X+ axis along the XZ plane.
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function vang(v) =
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len(v)==2? atan2(v.y,v.x) :
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let(res=xyz_to_spherical(v)) [res[1], 90-res[2]];
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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 = [0:1: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 = [0:1: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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// Example:
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// vabs([-1,3,-9]); // Returns: [1,3,9]
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function vabs(v) = [for (x=v) abs(x)];
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// Function: unit()
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// Description:
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// Returns unit length normalized version of vector v.
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// If passed a zero-length vector, returns the unchanged vector.
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// Arguments:
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// v = The vector to normalize.
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// Examples:
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// unit([10,0,0]); // Returns: [1,0,0]
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// unit([0,10,0]); // Returns: [0,1,0]
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// unit([0,0,10]); // Returns: [0,0,1]
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// unit([0,-10,0]); // Returns: [0,-1,0]
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// unit([0,0,0]); // Returns: [0,0,0]
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function unit(v) = norm(v)<=EPSILON? 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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// vector_angle(PT1,PT2,PT3);
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// vector_angle([PT1,PT2,PT3]);
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// Description:
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// If given a single list of two vectors, like `vector_angle([V1,V2])`, returns the angle between the two vectors V1 and V2.
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// If given a single list of three points, like `vector_angle([A,B,C])`, returns the angle between the line segments AB and BC.
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// If given two vectors, like `vector_angle(V1,V2)`, returns the angle between the two vectors V1 and V2.
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// If given three points, like `vector_angle(A,B,C)`, returns the angle between the line segments AB and BC.
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// Arguments:
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// v1 = First vector or point.
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// v2 = Second vector or point.
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// v3 = Third point in three point mode.
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// Examples:
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// vector_angle(UP,LEFT); // Returns: 90
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// vector_angle(RIGHT,LEFT); // Returns: 180
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// vector_angle(UP+RIGHT,RIGHT); // Returns: 45
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// vector_angle([10,10], [0,0], [10,-10]); // Returns: 90
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// vector_angle([10,0,10], [0,0,0], [-10,10,0]); // Returns: 120
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// vector_angle([[10,0,10], [0,0,0], [-10,10,0]]); // Returns: 120
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function vector_angle(v1,v2=undef,v3=undef) =
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(is_list(v1) && is_list(v1[0]) && is_undef(v2) && is_undef(v3))? (
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assert(is_vector(v1.x))
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assert(is_vector(v1.y))
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len(v1)==3? assert(is_vector(v1.z)) vector_angle(v1.x, v1.y, v1.z) :
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len(v1)==2? vector_angle(v1.x, v1.y) :
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assert(false, "Bad arguments.")
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) :
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(is_vector(v1) && is_vector(v2) && is_vector(v3))? vector_angle(v1-v2, v3-v2) :
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(is_vector(v1) && is_vector(v2) && is_undef(v3))? (
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assert(len(v1)==len(v2))
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// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
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acos(constrain((v1*v2)/(norm(v1)*norm(v2)), -1, 1))
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) : assert(false, "Bad arguments.");
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// Function: vector_axis()
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// Usage:
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// vector_axis(v1,v2);
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// vector_axis(PT1,PT2,PT3);
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// vector_axis([PT1,PT2,PT3]);
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// Description:
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// If given a single list of two vectors, like `vector_axis([V1,V2])`, returns the vector perpendicular the two vectors V1 and V2.
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// If given a single list of three points, like `vector_axis([A,B,C])`, returns the vector perpendicular the line segments AB and BC.
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// If given two vectors, like `vector_axis(V1,V1)`, returns the vector perpendicular the two vectors V1 and V2.
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// If given three points, like `vector_axis(A,B,C)`, returns the vector perpendicular the line segments AB and BC.
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// Arguments:
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// v1 = First vector or point.
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// v2 = Second vector or point.
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// v3 = Third point in three point mode.
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// Examples:
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// vector_axis(UP,LEFT); // Returns: [0,-1,0] (FWD)
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// vector_axis(RIGHT,LEFT); // Returns: [0,-1,0] (FWD)
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// vector_axis(UP+RIGHT,RIGHT); // Returns: [0,1,0] (BACK)
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// vector_axis([10,10], [0,0], [10,-10]); // Returns: [0,0,-1] (DOWN)
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// vector_axis([10,0,10], [0,0,0], [-10,10,0]); // Returns: [-0.57735, -0.57735, 0.57735]
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// vector_axis([[10,0,10], [0,0,0], [-10,10,0]]); // Returns: [-0.57735, -0.57735, 0.57735]
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function vector_axis(v1,v2=undef,v3=undef) =
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(is_list(v1) && is_list(v1[0]) && is_undef(v2) && is_undef(v3))? (
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assert(is_vector(v1.x))
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assert(is_vector(v1.y))
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len(v1)==3? assert(is_vector(v1.z)) vector_axis(v1.x, v1.y, v1.z) :
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len(v1)==2? vector_axis(v1.x, v1.y) :
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assert(false, "Bad arguments.")
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) :
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(is_vector(v1) && is_vector(v2) && is_vector(v3))? vector_axis(v1-v2, v3-v2) :
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(is_vector(v1) && is_vector(v2) && is_undef(v3))? 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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) unit(cross(v1,v3)) : assert(false, "Bad arguments.");
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// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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