mirror of
https://github.com/BelfrySCAD/BOSL2.git
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223 lines
9.3 KiB
OpenSCAD
223 lines
9.3 KiB
OpenSCAD
//////////////////////////////////////////////////////////////////////
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// LibFile: vectors.scad
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// Vector math functions.
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// Includes:
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// include <BOSL2/std.scad>
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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]);
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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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// zero = If false, require that the length/`norm()` of the vector is not approximately zero. If true, require the length/`norm()` of the vector to be approximately zero-length. Default: `undef` (don't check vector length/`norm()`.)
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// all_nonzero = If true, requires all elements of the vector to be more than `eps` different from zero. Default: `false`
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// eps = The minimum vector length that is considered non-zero. Default: `EPSILON` (`1e-9`)
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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([0,4,0],3,zero=false); // Returns true
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// is_vector([0,0,0],zero=false); // Returns false
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// is_vector([0,0,1e-12],zero=false); // Returns false
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// is_vector([0,1,0],all_nonzero=false); // Returns false
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// is_vector([1,1,1],all_nonzero=false); // Returns true
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// is_vector([],zero=false); // Returns false
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function is_vector(v, length, zero, all_nonzero=false, eps=EPSILON) =
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is_list_of(v,1) // is_list(v) && is_num(v[0]) && is_num(0*(v*v))
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&& len(v)>0
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&& (is_undef(length) || len(v)==length)
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&& (is_undef(zero) || ((norm(v) >= eps) == !zero))
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&& (!all_nonzero || all_nonzero(v)) ;
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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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assert( is_vector(v,2) || is_vector(v,3) , "Invalid vector")
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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 multiplication. Multiplies each element of `v1` by the corresponding element of `v2`.
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// Both `v1` and `v2` must be the same length. 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) =
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assert( is_list(v1) && is_list(v2) && len(v1)==len(v2), "Incompatible input")
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[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) =
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assert( is_vector(v1) && is_vector(v2,len(v1)), "Incompatible vectors")
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[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) =
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assert( is_vector(v), "Invalid vector" )
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[for (x=v) abs(x)];
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// Function: vfloor()
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// Description:
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// Returns the given vector after performing a `floor()` on all items.
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function vfloor(v) =
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assert( is_vector(v), "Invalid vector" )
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[for (x=v) floor(x)];
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// Function: vceil()
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// Description:
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// Returns the given vector after performing a `ceil()` on all items.
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function vceil(v) =
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assert( is_vector(v), "Invalid vector" )
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[for (x=v) ceil(x)];
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// Function: unit()
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// Usage:
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// unit(v, [error]);
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// Description:
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// Returns the unit length normalized version of vector v. If passed a zero-length vector,
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// asserts an error unless `error` is given, in which case the value of `error` is returned.
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// Arguments:
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// v = The vector to normalize.
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// error = If given, and input is a zero-length vector, this value is returned. Default: Assert error on zero-length vector.
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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],[1,2,3]); // Returns: [1,2,3]
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// unit([0,0,0]); // Asserts an error.
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function unit(v, error=[[["ASSERT"]]]) =
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assert(is_vector(v), str("Expected a vector. Got: ",v))
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norm(v)<EPSILON? (error==[[["ASSERT"]]]? assert(norm(v)>=EPSILON,"Tried to normalize a zero vector") : error) :
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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([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,v3) =
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assert( ( is_undef(v3) && ( is_undef(v2) || same_shape(v1,v2) ) )
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|| is_consistent([v1,v2,v3]) ,
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"Bad arguments.")
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assert( is_vector(v1) || is_consistent(v1), "Bad arguments.")
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let( vecs = ! is_undef(v3) ? [v1-v2,v3-v2] :
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! is_undef(v2) ? [v1,v2] :
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len(v1) == 3 ? [v1[0]-v1[1], v1[2]-v1[1]]
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: v1
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)
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assert(is_vector(vecs[0],2) || is_vector(vecs[0],3), "Bad arguments.")
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let(
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norm0 = norm(vecs[0]),
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norm1 = norm(vecs[1])
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)
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assert(norm0>0 && norm1>0, "Zero length vector.")
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// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
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acos(constrain((vecs[0]*vecs[1])/(norm0*norm1), -1, 1));
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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([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 to the plane through a, B and C.
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// If given two vectors, like `vector_axis(V1,V2)`, returns the vector perpendicular to the two vectors V1 and V2.
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// If given three points, like `vector_axis(A,B,C)`, returns the vector perpendicular to the plane through a, B and C.
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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_vector(v3)
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? assert(is_consistent([v3,v2,v1]), "Bad arguments.")
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vector_axis(v1-v2, v3-v2)
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: assert( is_undef(v3), "Bad arguments.")
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is_undef(v2)
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? assert( is_list(v1), "Bad arguments.")
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len(v1) == 2
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? vector_axis(v1[0],v1[1])
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: vector_axis(v1[0],v1[1],v1[2])
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: assert( is_vector(v1,zero=false) && is_vector(v2,zero=false) && is_consistent([v1,v2])
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, "Bad arguments.")
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let(
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eps = 1e-6,
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w1 = point3d(v1/norm(v1)),
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w2 = point3d(v2/norm(v2)),
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w3 = (norm(w1-w2) > eps && norm(w1+w2) > eps) ? w2
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: (norm(vabs(w2)-UP) > eps)? UP
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: RIGHT
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) unit(cross(w1,w3));
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// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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