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Added add_scalar(). Fixed normalize() for [0,0]. Added examples for vector functions.
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Revar Desmera
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1 changed files with 78 additions and 3 deletions
81
vectors.scad
81
vectors.scad
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@ -16,9 +16,32 @@
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// is_vector(v)
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// Description:
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// Returns true if the given value is a list, and at least the first item is a number.
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// Example:
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// is_vector([1,2,3]); // Returns: true
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// is_vector([[1,2,3]]); // Returns: false
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// is_vector(["foo"]); // Returns: false
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// is_vector([]); // Returns: false
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// is_vector(1); // Returns: false
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// is_vector("foo"); // Returns: false
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// is_vector(true); // Returns: false
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function is_vector(v) = is_list(v) && is_num(v[0]);
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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: 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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@ -47,6 +70,8 @@ function vdiv(v1, v2) = [for (i = [0:1:len(v1)-1]) v1[i]/v2[i]];
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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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@ -56,7 +81,13 @@ function vabs(v) = [for (x=v) abs(x)];
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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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function normalize(v) = v==[0,0,0]? v : v/norm(v);
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// Examples:
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// normalize([10,0,0]); // Returns: [1,0,0]
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// normalize([0,10,0]); // Returns: [0,1,0]
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// normalize([0,0,10]); // Returns: [0,0,1]
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// normalize([0,-10,0]); // Returns: [0,-1,0]
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// normalize([0,0,0]); // Returns: [0,0,0]
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function normalize(v) = norm(v)<=EPSILON? v : v/norm(v);
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// Function: vquant()
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@ -67,6 +98,16 @@ function normalize(v) = v==[0,0,0]? v : v/norm(v);
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// Arguments:
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// v = The vector to quantize.
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// m = The multiple to quantize to.
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// Examples:
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// vquant(12,4); // Returns: 12
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// vquant(13,4); // Returns: 12
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// vquant(14,4); // Returns: 16
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// vquant(15,4); // Returns: 16
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// vquant(16,4); // Returns: 16
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// vquant(9,3); // Returns: 9
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// vquant(10,3); // Returns: 9
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// vquant(11,3); // Returns: 12
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// vquant(12,3); // Returns: 12
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function vquant(v,m) = [for (x=v) quant(x,m)];
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@ -78,6 +119,16 @@ function vquant(v,m) = [for (x=v) quant(x,m)];
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// Arguments:
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// v = The vector to quantize.
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// m = The multiple to quantize to.
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// Examples:
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// vquant(12,4); // Returns: 12
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// vquant(13,4); // Returns: 12
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// vquant(14,4); // Returns: 12
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// vquant(15,4); // Returns: 12
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// vquant(16,4); // Returns: 16
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// vquant(9,3); // Returns: 9
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// vquant(10,3); // Returns: 9
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// vquant(11,3); // Returns: 9
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// vquant(12,3); // Returns: 12
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function vquantdn(v,m) = [for (x=v) quantdn(x,m)];
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@ -89,6 +140,16 @@ function vquantdn(v,m) = [for (x=v) quantdn(x,m)];
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// Arguments:
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// v = The vector to quantize.
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// m = The multiple to quantize to.
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// Examples:
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// vquant(12,4); // Returns: 12
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// vquant(13,4); // Returns: 16
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// vquant(14,4); // Returns: 16
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// vquant(15,4); // Returns: 16
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// vquant(16,4); // Returns: 16
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// vquant(9,3); // Returns: 9
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// vquant(10,3); // Returns: 12
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// vquant(11,3); // Returns: 12
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// vquant(12,3); // Returns: 12
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function vquantup(v,m) = [for (x=v) quantup(x,m)];
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@ -100,13 +161,19 @@ function vquantup(v,m) = [for (x=v) quantup(x,m)];
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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,V1)`, returns the angle between the two vectors V1 and V2.
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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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// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
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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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@ -116,6 +183,7 @@ function vector_angle(v1,v2=undef,v3=undef) =
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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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// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
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(is_vector(v1) && is_vector(v2) && is_undef(v3))? acos(constrain((v1*v2)/(norm(v1)*norm(v2)), -1, 1)) :
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assert(false, "Bad arguments.");
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@ -134,6 +202,13 @@ function vector_angle(v1,v2=undef,v3=undef) =
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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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