Ellipse Intersecting Line by STxAxTIC

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The Librarian:
Ellipse Intersecting Line

Author: @STxAxTIC
Source: qb64.org Forum
URL: https://www.qb64.org/forum/index.php?topic=2143.0
Version: 2020
Tags: [2d], [geometry], [intersections]

Description:
In response to

https://www.qb64.org/forum/index.php?topic=2132

... all I could think is "why stop at circles when you can do ellipses?"

Source Code:

--- Code: QB64: ---SCREEN 12 xorig = 0yorig = 0 CALL cline(xorig, yorig, xorig + _WIDTH, yorig, 8)CALL cline(xorig, yorig, xorig + -_WIDTH, yorig, 8)CALL cline(xorig, yorig, xorig, yorig + _HEIGHT, 8)CALL cline(xorig, yorig, xorig, yorig - _HEIGHT, 8) xzoom = 20yzoom = 20 ' Initialize lineb = -2d = 2lineang = .1vx = COS(lineang)vy = SIN(lineang)m = vy / vx ' Initialize ellipsex0 = 2y0 = -2ellipsearg = .2amag = 10ax = amag * COS(ellipsearg)ay = amag * SIN(ellipsearg)bmag = 5bx = bmag * COS(ellipsearg + 3.14 / 2)by = bmag * SIN(ellipsearg + 3.14 / 2) DO DO WHILE _MOUSEINPUT x = _MOUSEX y = _MOUSEY IF ((x > 0) AND (x < _WIDTH) AND (y > 0) AND (y < _HEIGHT)) THEN IF _MOUSEBUTTON(1) THEN x = _MOUSEX y = _MOUSEY x0 = (x - _WIDTH / 2) / xzoom y0 = (-y + _HEIGHT / 2) / yzoom END IF IF _MOUSEBUTTON(2) THEN x = _MOUSEX y = _MOUSEY d = (x - _WIDTH / 2) / xzoom b = (-y + _HEIGHT / 2) / yzoom END IF IF _MOUSEWHEEL > 0 THEN lineang = lineang + .01 vx = COS(lineang) vy = SIN(lineang) m = vy / vx END IF IF _MOUSEWHEEL < 0 THEN lineang = lineang - .01 vx = COS(lineang) vy = SIN(lineang) m = vy / vx END IF END IF LOOP SELECT CASE _KEYHIT CASE 18432 bmag = bmag + .1 bx = bmag * COS(ellipsearg + 3.14 / 2) by = bmag * SIN(ellipsearg + 3.14 / 2) CASE 20480 bmag = bmag - .1 bx = bmag * COS(ellipsearg + 3.14 / 2) by = bmag * SIN(ellipsearg + 3.14 / 2) CASE 19200 ellipsearg = ellipsearg - .1 ax = amag * COS(ellipsearg) ay = amag * SIN(ellipsearg) bx = bmag * COS(ellipsearg + 3.14 / 2) by = bmag * SIN(ellipsearg + 3.14 / 2) CASE 19712 ellipsearg = ellipsearg + .1 ax = amag * COS(ellipsearg) ay = amag * SIN(ellipsearg) bx = bmag * COS(ellipsearg + 3.14 / 2) by = bmag * SIN(ellipsearg + 3.14 / 2) END SELECT ' Intersections a2 = ax ^ 2 + ay ^ 2 b2 = bx ^ 2 + by ^ 2 av = ax * vx + ay * vy bv = bx * vx + by * vy rbx = d - x0 rby = b - y0 adbr = ax * rbx + ay * rby bdbr = bx * rbx + by * rby aa = av ^ 2 / a2 ^ 2 + bv ^ 2 / b2 ^ 2 bb = 2 * (av * adbr / a2 ^ 2 + bv * bdbr / b2 ^ 2) cc = adbr ^ 2 / a2 ^ 2 + bdbr ^ 2 / b2 ^ 2 - 1 arg = bb ^ 2 - 4 * aa * cc IF (arg > 0) THEN alpha1 = (-bb + SQR(arg)) / (2 * aa) alpha2 = (-bb - SQR(arg)) / (2 * aa) x1 = alpha1 * vx + d x2 = alpha2 * vx + d y1 = alpha1 * vy + b y2 = alpha2 * vy + b ELSE x1 = -999 y1 = -999 x2 = -999 y2 = -999 END IF GOSUB draweverything _LIMIT 60 _DISPLAYLOOP END draweverything:CLSPAINT (1, 1), 15COLOR 0, 15LOCATE 1, 1: PRINT "LClick=Move ellipse, RClick=Move line, Scroll=Tilt line, Arrows=Shift ellipse"FOR alpha = -20 TO 20 STEP .001 x = alpha * vx + d y = alpha * vy + b CALL ccircle(xorig + x * xzoom, yorig + y * yzoom, 1, 1)NEXTFOR t = 0 TO 6.284 STEP .001 x = x0 + ax * COS(t) + bx * SIN(t) y = y0 + ay * COS(t) + by * SIN(t) CALL ccircle(xorig + x * xzoom, yorig + y * yzoom, 1, 4)NEXTCALL ccircle(xorig + x1 * xzoom, yorig + y1 * yzoom, 10, 1)CALL ccircle(xorig + x2 * xzoom, yorig + y2 * yzoom, 10, 1)RETURN SUB cline (x1, y1, x2, y2, col) LINE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2)-(_WIDTH / 2 + x2, -y2 + _HEIGHT / 2), colEND SUB SUB ccircle (x1, y1, r, col) CIRCLE (_WIDTH / 2 + x1, -y1 + _HEIGHT / 2), r, colEND SUB

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