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;;;; utils.lisp
(in-package #:wheelwork)
(define-symbol-macro +pi-over-180+ 0.017453292519943295d0)
(defun radians (degrees)
"Converse DEGREES to radians"
(* degrees +pi-over-180+))
(defun safe-slot (object slot &optional default)
(if-let (val (and (slot-exists-p object slot)
(slot-boundp object slot)
(slot-value object slot)))
val
default))
(defun counterclockwisep (a b c)
"A B and C are vectors created by 3d-vectors:vec, each representing
a 2d point. Returns T if the three are supplied in counterclockwise
order, nil if not."
(> (* (- (vec:vx b) (vec:vx a))
(- (vec:vy c) (vec:vy a)))
(* (- (vec:vy b) (vec:vy a))
(- (vec:vx c) (vec:vx a)))))
(defun segments-intersect-p (a b c d)
"A B C and D are vectors of the sort created by 3d-vectors:vec,
each representing a 2d point. Returns T if the line segment between A
and B intersects the linesegment between C and D, NIL otherwise."
(or (vec:v= a c) (vec:v= a d) (vec:v= b c) (vec:v= b d)
(and (not (eq (counterclockwisep a c d) (counterclockwisep b c d)))
(not (eq (counterclockwisep a b c) (counterclockwisep a b d))))))
(defun paths-intersect-p (path-a path-b)
"Paths are lists of vectors, each of which represents a 2d point."
(loop for (a1 a2 . more-a) on path-a
while a2
thereis (loop for (b1 b2 . b-more) on path-b
while b2
thereis (segments-intersect-p a1 a2 b1 b2))))
(defun closed-path-p (path)
(equalp (first path)
(first (last path))))
(defun path-encloses-point-p (path pt)
"Path is a list of vectors, pt is a single vector."
(assert (closed-path-p path) () "Enclosing path must be a closed path.")
(let* ((bounds
(path-bounds path))
(corner
;; creating a point guaranteed to be outside of the path
(vec:vec (- (getf bounds :left) (getf bounds :width))
(- (getf bounds :bottom) (getf bounds :height))
0.0 1.0)))
(loop for (p1 p2 . more) on path
while p2
when (segments-intersect-p p1 p2 pt corner)
count 1 into intersection-count
finally
(return (oddp intersection-count)))))
(defun path-encloses-path-p (path-a path-b)
"T if path-b is totally contained in path-a and does not intersect path-a"
(assert (closed-path-p path-a) () "Enclosing path must be a closed path.")
(and
(loop for (p1 p2 . more) on path-b
while p2
always (path-encloses-point-p path-a p1))
(not (paths-intersect-p path-a path-b))))
(defun path-bounds (path)
"Path is a list of vectors representing 2d points. Returns the
bounds and width and height as a plist of the form
(:top N :left N :right N :bottom N :width N :height N)
This is the smallest UNROTATED RECTANGLE that contains the points in
the path."
(loop
with max-x = nil
and max-y = nil
and min-x = nil
and min-y = nil
for vec in path
for x = (vec:vx vec)
for y = (vec:vy vec)
when (or (null max-x) (< max-x x))
do (setf max-x x)
when (or (null min-x) (< x min-x))
do (setf min-x x)
when (or (null max-y) (< max-y y))
do (setf max-y y)
when (or (null min-y) (< y min-y))
do (setf min-y y)
finally
(return (list :top max-y :left min-x :right max-x :bottom min-y
:width (- max-x min-x)
:height (- max-y min-y)))))
(defmacro setf-many (&rest places-and-value)
"e.g. (setf-many a b c 10) would set a b and c to 10"
(let* ((value-form
(first (last places-and-value)))
(value
(gensym))
(clauses
(loop for place in (butlast places-and-value)
append `(,place ,value))))
`(let ((,value ,value-form))
(setf ,@clauses))))
(defun euclidean-dist (x1 y1 x2 y2)
(let ((dx (- x2 x1))
(dy (- y2 y1)))
(sqrt (+ (* dx dx) (* dy dy)))))
(let ((cache
(make-array 100 :adjustable t :initial-element nil)))
(defun factorial (n)
(cond
((zerop n) 1)
((< n (length cache))
(or (aref cache n)
(setf (aref cache n)
(* n (factorial (1- n))))))
((>= n (length cache))
(setf cache (adjust-array cache (* 2 (length cache))))
(factorial n)))))
(defun binomial-coefficient (n k)
(/ (factorial n)
(* (factorial k) (factorial (- n k)))))
(defun bezier-lambda (&rest points)
(let* ((n
(1- (length points)))
(bin-coeffs
(loop for i from 0 to n collect (binomial-coefficient n i))))
(lambda (a)
(loop for (x y) in points
for i from 0
for bin-coeff in bin-coeffs
for coeff = (* bin-coeff
(expt (- 1 a) (- n i))
(expt a i))
sum (* coeff x) into bx
sum (* coeff y) into by
finally (return (list bx by))))))
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