BOSL2/vectors.scad

//////////////////////////////////////////////////////////////////////
// LibFile: vectors.scad
//   Vector math functions.
//   To use, add the following lines to the beginning of your file:
//   ```
//   use <BOSL2/std.scad>
//   ```
//////////////////////////////////////////////////////////////////////


// Section: Vector Manipulation


// Function: is_vector()
// Usage:
//   is_vector(v)
// Description:
//   Returns true if the given value is a list, and at least the first item is a number.
function is_vector(v) = is_list(v) && is_num(v[0]);


// 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 = [0:1: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 = [0:1: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: vquant()
// Usage:
//   vquant(v,m)
// Description:
//   Quantizes each scalar in the vector `v` to an integer multiple of `m`, rounding to the nearest multiple.
// Arguments:
//   v = The vector to quantize.
//   m = The multiple to quantize to.
function vquant(v,m) = [for (x=v) quant(x,m)];


// Function: vquantdn()
// Usage:
//   vquantdn(v,m)
// Description:
//   Quantizes each scalar in the vector `v` to an integer multiple of `m`, rounding down to the nearest multiple.
// Arguments:
//   v = The vector to quantize.
//   m = The multiple to quantize to.
function vquantdn(v,m) = [for (x=v) quantdn(x,m)];


// Function: vquantup()
// Usage:
//   vquantup(v,m)
// Description:
//   Quantizes each scalar in the vector `v` to an integer multiple of `m`, rounding up to the nearest multiple.
// Arguments:
//   v = The vector to quantize.
//   m = The multiple to quantize to.
function vquantup(v,m) = [for (x=v) quantup(x,m)];


// Function: vector_angle()
// Usage:
//   vector_angle(v1,v2);
//   vector_angle(PT1,PT2,PT3);
//   vector_angle([PT1,PT2,PT3]);
// Description:
//   If given a single list of two vectors, like `vector_angle([V1,V2])`, returns the angle between the two vectors V1 and V2.
//   If given a single list of three points, like `vector_angle([A,B,C])`, returns the angle between the line segments AB and BC.
//   If given two vectors, like `vector_angle(V1,V1)`, returns the angle between the two vectors V1 and V2.
//   If given three points, like `vector_angle(A,B,C)`, returns the angle between the line segments AB and BC.
// Arguments:
//   v1 = First vector or point.
//   v2 = Second vector or point.
//   v3 = Third point in three point mode.
// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
function vector_angle(v1,v2=undef,v3=undef) =
	(is_list(v1) && is_list(v1[0]) && is_undef(v2) && is_undef(v3))? (
		assert(is_vector(v1.x))
		assert(is_vector(v1.y))
		len(v1)==3? assert(is_vector(v1.z)) vector_angle(v1.x, v1.y, v1.z) :
		len(v1)==2? vector_angle(v1.x, v1.y) :
		assert(false, "Bad arguments.")
	) :
	(is_vector(v1) && is_vector(v2) && is_vector(v3))? vector_angle(v1-v2, v3-v2) :
	(is_vector(v1) && is_vector(v2) && is_undef(v3))? acos(constrain((v1*v2)/(norm(v1)*norm(v2)), -1, 1)) :
	assert(false, "Bad arguments.");


// Function: vector_axis()
// Usage:
//   vector_axis(v1,v2);
//   vector_axis(PT1,PT2,PT3);
//   vector_axis([PT1,PT2,PT3]);
// Description:
//   If given a single list of two vectors, like `vector_axis([V1,V2])`, returns the vector perpendicular the two vectors V1 and V2.
//   If given a single list of three points, like `vector_axis([A,B,C])`, returns the vector perpendicular the line segments AB and BC.
//   If given two vectors, like `vector_axis(V1,V1)`, returns the vector perpendicular the two vectors V1 and V2.
//   If given three points, like `vector_axis(A,B,C)`, returns the vector perpendicular the line segments AB and BC.
// Arguments:
//   v1 = First vector or point.
//   v2 = Second vector or point.
//   v3 = Third point in three point mode.
function vector_axis(v1,v2=undef,v3=undef) =
	(is_list(v1) && is_list(v1[0]) && is_undef(v2) && is_undef(v3))? (
		assert(is_vector(v1.x))
		assert(is_vector(v1.y))
		len(v1)==3? assert(is_vector(v1.z)) vector_axis(v1.x, v1.y, v1.z) :
		len(v1)==2? vector_axis(v1.x, v1.y) :
		assert(false, "Bad arguments.")
	) :
	(is_vector(v1) && is_vector(v2) && is_vector(v3))? vector_axis(v1-v2, v3-v2) :
	(is_vector(v1) && is_vector(v2) && is_undef(v3))? 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)) : assert(false, "Bad arguments.");


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