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;;;; utils.lisp
(in-package #:wheelwork)
(declaim (inline radians counterclockwisep points-equal-p))
(defun radians (degrees)
"Converse DEGREES to radians"
(* degrees 0.017453292519943295d0))
(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 (ax ay bx by cx cy)
"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."
(> (* (- bx ax)
(- cy ay))
(* (- by ay)
(- cx ax))))
(defun points-equal-p (x1 y1 x2 y2)
(and (= x1 x2)) (= y1 y2))
(defun segments-intersect-p (ax ay bx by cx cy dx dy)
"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 (points-equal-p ax ay cx cy)
(points-equal-p ax ay dx dy)
(points-equal-p bx by cx cy)
(points-equal-p bx by dx dy)
(and (not (eq (counterclockwisep ax ay cx cy dx dy)
(counterclockwisep bx by cx cy dx dy)))
(not (eq (counterclockwisep ax ay bx by cx cy)
(counterclockwisep ax ay bx by dx dy))))))
(defun paths-intersect-p (path1 path2)
"Paths are lists of vectors, each of which represents a 2d point."
(loop for ((ax ay) (bx by) . more1) on path1
while bx
thereis (loop for ((cx cy) (dx dy) . more2) on path2
while dx
thereis (segments-intersect-p ax ay bx by cx cy dx dy))))
(defun closed-path-p (path)
(equalp (first path)
(first (last path))))
(defun path-encloses-point-p (path px py)
"Path is a list of points, 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
(list (- (getf bounds :left) (getf bounds :width))
(- (getf bounds :bottom) (getf bounds :height)))))
(loop
with (cx cy) = corner
for ((ax ay) (bx by) . more) on path
while bx
when (segments-intersect-p ax ay bx by px py cx cy)
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 (x y) in path
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))))))
(defun clamp (lo val hi)
"Returns VAL if (< LO VAL HI), otherwise returns LO or HI depending
on which boundary VAL is outside of."
(max lo (min val hi)))
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