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, [length]);
// Description:
//   Returns true if v is a list of finite numbers.
// Arguments:
//   v = The value to test to see if it is a vector.
//   length = If given, make sure the vector is `length` items long.
//   zero = If false, require that the length of the vector is not approximately zero.  If true, require the length of the vector to be approximately zero-length.  Default: `undef` (don't check vector length.)
//   eps = The minimum vector length that is considered non-zero.  Default: `EPSILON` (`1e-9`)
// Example:
//   is_vector(4);                          // Returns false
//   is_vector([4,true,false]);             // Returns false
//   is_vector([3,4,INF,5]);                // Returns false
//   is_vector([3,4,5,6]);                  // Returns true
//   is_vector([3,4,undef,5]);              // Returns false
//   is_vector([3,4,5],3);                  // Returns true
//   is_vector([3,4,5],4);                  // Returns true
//   is_vector([]);                         // Returns false
//   is_vector([0,4,0],3,zero=false);     // Returns true
//   is_vector([0,0,0],zero=false);       // Returns false
//   is_vector([0,0,1e-12],zero=false);   // Returns false
//   is_vector([],zero=false);            // Returns false
function is_vector(v,length,zero,eps=EPSILON) =
    is_list(v) && is_num(0*(v*v))
    && (is_undef(length) || len(v)==length)
    && (is_undef(zero) || ((norm(v) >= eps) == !zero));


// Function: vang()
// Usage:
//   theta = vang([X,Y]);
//   theta_phi = vang([X,Y,Z]);
// Description:
//   Given a 2D vector, returns the angle in degrees counter-clockwise from X+ on the XY plane.
//   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.
function vang(v) =
    assert( is_vector(v,2) || is_vector(v,3) , "Invalid vector")
    len(v)==2? atan2(v.y,v.x) :
    let(res=xyz_to_spherical(v)) [res[1], 90-res[2]];


// Function: vmul()
// Description:
//   Element-wise vector multiplication.  Multiplies each element of vector `v1` by
//   the corresponding element of vector `v2`. The vectors should have the same dimension.
//   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) = 
    assert( is_vector(v1) && is_vector(v2,len(v1)), "Incompatible vectors")
    [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) = 
    assert( is_vector(v1) && is_vector(v2,len(v1)), "Incompatible vectors")
    [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.
// Example:
//   vabs([-1,3,-9]);  // Returns: [1,3,9]
function vabs(v) =
    assert( is_vector(v), "Invalid vector" ) 
    [for (x=v) abs(x)];


// Function: vfloor()
// Description:
//   Returns the given vector after performing a `floor()` on all items.
function vfloor(v) =
    assert( is_vector(v), "Invalid vector" ) 
    [for (x=v) floor(x)];


// Function: vceil()
// Description:
//   Returns the given vector after performing a `ceil()` on all items.
function vceil(v) =
    assert( is_vector(v), "Invalid vector" ) 
    [for (x=v) ceil(x)];


// Function: unit()
// Usage:
//   unit(v, [error]);
// Description:
//   Returns the unit length normalized version of vector v.  If passed a zero-length vector,
//   asserts an error unless `error` is given, in which case the value of `error` is returned.
// Arguments:
//   v = The vector to normalize.
//   error = If given, and input is a zero-length vector, this value is returned.  Default: Assert error on zero-length vector.
// Examples:
//   unit([10,0,0]);   // Returns: [1,0,0]
//   unit([0,10,0]);   // Returns: [0,1,0]
//   unit([0,0,10]);   // Returns: [0,0,1]
//   unit([0,-10,0]);  // Returns: [0,-1,0]
//   unit([0,0,0],[1,2,3]);    // Returns: [1,2,3]
//   unit([0,0,0]);    // Asserts an error.
function unit(v, error=[[["ASSERT"]]]) =
    assert(is_vector(v), str("Expected a vector.  Got: ",v))
    norm(v)<EPSILON? (error==[[["ASSERT"]]]? assert(norm(v)>=EPSILON) : error) :
    v/norm(v);


// Function: vector_angle()
// Usage:
//   vector_angle(v1,v2);
//   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,V2)`, 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.
// Examples:
//   vector_angle(UP,LEFT);     // Returns: 90
//   vector_angle(RIGHT,LEFT);  // Returns: 180
//   vector_angle(UP+RIGHT,RIGHT);  // Returns: 45
//   vector_angle([10,10], [0,0], [10,-10]);  // Returns: 90
//   vector_angle([10,0,10], [0,0,0], [-10,10,0]);  // Returns: 120
//   vector_angle([[10,0,10], [0,0,0], [-10,10,0]]);  // Returns: 120
function vector_angle(v1,v2,v3) =
    assert( ( is_undef(v3) && ( is_undef(v2) || same_shape(v1,v2) ) )
            || is_consistent([v1,v2,v3]) ,
            "Bad arguments.")
    assert( is_vector(v1) || is_consistent(v1), "Bad arguments.") 
    let( vecs = ! is_undef(v3) ? [v1-v2,v3-v2] :
                ! is_undef(v2) ? [v1,v2] :
                len(v1) == 3   ? [v1[0]-v1[1], v1[2]-v1[1]] 
                               : v1
    )
    assert(is_vector(vecs[0],2) || is_vector(vecs[0],3), "Bad arguments.")
    let(
        norm0 = norm(vecs[0]),
        norm1 = norm(vecs[1])
    )
    assert(norm0>0 && norm1>0, "Zero length vector.")
    // NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
    acos(constrain((vecs[0]*vecs[1])/(norm0*norm1), -1, 1));
    

// Function: vector_axis()
// Usage:
//   vector_axis(v1,v2);
//   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 to the plane through a, B and C.
//   If given two vectors, like `vector_axis(V1,V2)`, returns the vector perpendicular to the two vectors V1 and V2.
//   If given three points, like `vector_axis(A,B,C)`, returns the vector perpendicular to the plane through a, B and C.
// Arguments:
//   v1 = First vector or point.
//   v2 = Second vector or point.
//   v3 = Third point in three point mode.
// Examples:
//   vector_axis(UP,LEFT);     // Returns: [0,-1,0] (FWD)
//   vector_axis(RIGHT,LEFT);  // Returns: [0,-1,0] (FWD)
//   vector_axis(UP+RIGHT,RIGHT);  // Returns: [0,1,0] (BACK)
//   vector_axis([10,10], [0,0], [10,-10]);  // Returns: [0,0,-1] (DOWN)
//   vector_axis([10,0,10], [0,0,0], [-10,10,0]);  // Returns: [-0.57735, -0.57735, 0.57735]
//   vector_axis([[10,0,10], [0,0,0], [-10,10,0]]);  // Returns: [-0.57735, -0.57735, 0.57735]
function vector_axis(v1,v2=undef,v3=undef) =
    is_vector(v3)
    ?   assert(is_consistent([v3,v2,v1]), "Bad arguments.")
        vector_axis(v1-v2, v3-v2)
    :   assert( is_undef(v3), "Bad arguments.")
        is_undef(v2)
        ?   assert( is_list(v1), "Bad arguments.")
            len(v1) == 2 
            ?   vector_axis(v1[0],v1[1]) 
            :   vector_axis(v1[0],v1[1],v1[2])
        :   assert( is_vector(v1,zero=false) && is_vector(v2,zero=false) && is_consistent([v1,v2])
                    , "Bad arguments.")  
            let(
              eps = 1e-6,
              w1 = point3d(v1/norm(v1)),
              w2 = point3d(v2/norm(v2)),
              w3 = (norm(w1-w2) > eps && norm(w1+w2) > eps) ? w2 
                   : (norm(vabs(w2)-UP) > eps)? UP 
                   : RIGHT
            ) unit(cross(w1,w3));



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