; Copyright (C) 2010 Dave Griffiths : See LICENCE file

(include "../maths/vec.sc")
(include "line.sc")
(include "../maths/intersection.sc")

(define (sphere p r) (list 'sphere p r))
(define (sphere? s) (eq? (car s) 'sphere))
(define (sphere-pos l) (list-ref l 1))
(define (sphere-radius l) (list-ref l 2))

(define (sphere/line-dist s l)
    (vdist (sphere-pos s) (line-closest-point l (sphere-pos s))))
   
(define (sphere/line-intersect? s l)
   (< (sphere/line-dist s l) (sphere-radius s)))

(define (sphere/line-intersect s l)
  (if (sphere/line-intersect? s l)
      (let* ((lv (line-vec l))
	  	     (position (sphere-pos s))
             (a (vsq lv))
             (b (* 2 (+ (* (vx lv) (- (vx (line-start l)) (vx position)))
                        (* (vy lv) (- (vy (line-start l)) (vy position)))
                        (* (vz lv) (- (vz (line-start l)) (vz position))))))
             (c (- (+ (vsq position) (vsq (line-start l)))
                   (* 2 (+ (* (vx position) (vx (line-start l)))
                           (* (vy position) (vy (line-start l)))
                           (* (vz position) (vz (line-start l)))))
                   (sq (sphere-radius s))))
             (i (- (* b b) (* 4 a c))))
        (cond 
          ((< i 0) #f)
          (else
           (let ((t (if (eq? i 0)
                        (/ (- b) (* 2 a)) ; grazing
                        (/ (- (- b) (sqrt (- (* b b) (* 4 a c)))) (* 2 a))))) ; just first intersection
             (if (and (> t 0) (< t 1))
                 (let ((pos (vadd (line-start l) (vmul lv t))))
                   (intersection t pos (vnorm (vsub pos position))))
                 #f)))))
      #f))