Topic: AcGeVecto2d::mirror

[pkohut]

Ok, this one has me stumped and getting nowhere.  Can someone explain how this is implemented? Thanks

AcGeVector2d & mirror(const AcGeVector2d & line);

line - Input line
Returns the 2D vector which is the result of mirroring of this vector with respect to 2D line line in the same plane.

2d vectors v1, v2, v3
v1.set(2.0, 2.0); v2.set(0.0, 0.0)
result of v1.mirror(v2) = {0.0, 0.0}

v1.set(2.0, 2.0); v2.set(1.0, 1.0)
result of v1.mirror(v2) = {4.0, 4.0}

v1.set(2.0, 2.0); v2.set(2.0, 2.0)
result of v1.mirror(v2) = {16.0, 16.0}

v1.set(2.0, 2.0); v2.set(3.0, 3.0)
result of v1.mirror(v2) = {36.0, 36.0}

v1.set(2.0, 3.0); v2.set(4.0, 5.0)
result of v1.mirror(v2) = {102.0, 107.0}

[gile]

Hi,

As far as can read C++ (and it's not far at all) and from what I can see with the examples you provide, it seems to me that the result coordinates are:
v3.X = (scalar * v2.X) - (area * v2.Y);
v3.Y = (scalar * v2.Y) + (area * v2.X);
where:
scalar is the scalar product (or dot product) of v1 v2:
(v1.X * v2.X) + (v1.Y * v2.Y)
area is the algebraic (signed) area of the triangle descibed by the 2 vectors:
(v1.X * v2.Y) - (v1.Y * v2.X)

As we're in a LISP forum, her're two ways to implement this 'mirror' function

Code: [Select]

(defun mirror (v1 v2)
  ((lambda (s a)
     (list (- (* s (car v2)) (* a (cadr v2)))
   (+ (* s (cadr v2)) (* a (car v2))))
   )
    (+ (* (car v1) (car v2)) (* (cadr v1) (cadr v2))) ; scalar product
    (- (* (car v1) (cadr v2)) (* (cadr v1) (car v2))) ; algebric area
  )
)

(defun mirror (v1 v2)
  ((lambda (x1 x2 y1 y2)
     (list
       (+ (* x1 (- (* x2 x2) (* y2 y2))) (* 2 x2 y1 y2))
       (+ (* y1 (- (* y2 y2) (* x2 x2))) (* 2 x1 x2 y2))
     )
   )
    (car v1)
    (car v2)
    (cadr v1)
    (cadr v2)
  )
)

[pkohut]

As we're in a LISP forum, her're two ways to implement this 'mirror' function

Again, thank you Gile.  I posted these in the lisp forum cause that's were most of the math brain power is    Here's C++ versions for those interested.

Code: [Select]

double DotPerp(const AcGeVector2d & v1, const AcGeVector2d & v2)
{
    return v1.x * v2.y - v1.y * v2.x;
}

AcGeVector2d Mirror(const AcGeVector2d & v1, const AcGeVector2d & v2)
{
    double dotProd = v1.dotProduct(v2);
    double dotPerp = DotPerp(v1, v2);

    return AcGeVector2d(dotProd * v2.x - dotPerp * v2.y, dotProd * v2.y + dotPerp * v2.x);

}