Circle Intersecting Line by bplus

[The Librarian]

Circle Intersecting Line

Author: @bplus
Source: qb64.org Forum
URL: https://www.qb64.org/forum/index.php?topic=2132.0
Version: 2020
Tags: [2d], [geometry], [intersections]

Description:
This is an interactive (mouse-driven) demo that calculates the intersection of any line with any circle.

Source Code:

Code: QB64: [Select]

1. _TITLE "Circle Intersect Line" ' b+ 2020-01-31 develop
2. ' Find point on line perpendicular to line at another point" 'B+ 2019-12-15
3. ' further for a Line and Circle Intersect, making full use of the information from the link below.
4.  
5. CONST xmax = 800, ymax = 600
6. SCREEN _NEWIMAGE(xmax, ymax, 32)
7. _SCREENMOVE 300, 40
8.  
9. DO
10.     CLS
11.     IF testTangent = 0 THEN 'test plug in set of border conditions not easy to click
12.         PRINT "First set here is a plug in test set for vertical lines."
13.         mx(1) = 200: my(1) = 100: mx(2) = 200: my(2) = 400 'line  x = 200
14.         mx(3) = 400: my(3) = 300: mx(4) = 150: my(4) = 300 ' circle origin (center 400, 300) then radius test 200 tangent, 150 more than tangent, 250 short
15.         FOR i = 1 TO 4
16.             CIRCLE (mx(i), my(i)), 2
17.         NEXT
18.         IF mx(1) <> mx(2) THEN
19.             slopeYintersect mx(1), my(1), mx(2), my(2), m, Y0 ' Y0 otherwise know as y Intersect
20.             LINE (0, Y0)-(xmax, m * xmax + Y0), &HFF0000FF
21.             LINE (mx(1), my(1))-(mx(2), my(2))
22.         ELSE
23.             LINE (mx(1), 0)-(mx(1), ymax), &HFF0000FF
24.             LINE (mx(1), my(1))-(mx(2), my(2))
25.         END IF
26.         testTangent = 1
27.     ELSE
28.         PRINT "First 2 clicks will form a line, 3rd the circle origin and 4th the circle radius:"
29.         WHILE pi < 4 'get 4 mouse clicks
30.             _PRINTSTRING (20, 20), SPACE$(20)
31.             _PRINTSTRING (20, 20), "Need 4 clicks, have" + STR$(pi)
32.             WHILE _MOUSEINPUT: WEND
33.             IF _MOUSEBUTTON(1) AND oldMouse = 0 THEN 'new mouse down
34.                 pi = pi + 1
35.                 mx(pi) = _MOUSEX: my(pi) = _MOUSEY
36.                 CIRCLE (mx(pi), my(pi)), 2
37.                 IF pi = 2 THEN 'draw first line segment then line
38.                     IF mx(1) <> mx(2) THEN
39.                         slopeYintersect mx(1), my(1), mx(2), my(2), m, Y0 ' Y0 otherwise know as y Intersect
40.                         LINE (0, Y0)-(xmax, m * xmax + Y0), &HFF0000FF
41.                         LINE (mx(1), my(1))-(mx(2), my(2))
42.                     ELSE
43.                         LINE (mx(1), 0)-(mx(1), ymax), &HFF0000FF
44.                         LINE (mx(1), my(1))-(mx(2), my(2))
45.                     END IF
46.                 END IF
47.             END IF
48.             oldMouse = _MOUSEBUTTON(1)
49.             _DISPLAY
50.             _LIMIT 60
51.         WEND
52.     END IF
53.     p = mx(3): q = my(3)
54.     r = SQR((mx(3) - mx(4)) ^ 2 + (my(3) - my(4)) ^ 2)
55.     CIRCLE (p, q), r, &HFFFF0000
56.     IF mx(1) = mx(2) THEN 'line is vertical so if r =
57.         IF r = ABS(mx(1) - mx(3)) THEN ' one point tangent intersect
58.             PRINT "Tangent point is "; TS$(mx(1)); ", "; TS$(my(3))
59.             CIRCLE (mx(1), my(3)), 2, &HFFFFFF00
60.             CIRCLE (mx(1), my(3)), 4, &HFFFFFF00
61.         ELSEIF r < ABS(mx(1) - mx(3)) THEN 'no intersect
62.             PRINT "No intersect, radius too small."
63.         ELSE '2 point intersect
64.             ydist = SQR(r ^ 2 - (mx(1) - mx(3)) ^ 2)
65.             y1 = my(3) + ydist
66.             y2 = my(3) - ydist
67.             PRINT "2 Point intersect (x1, y1) = "; TS$(mx(1)); ", "; TS$(y1); "  (x2, y2) = "; TS$(mx(1)); ", "; TS$(y2)
68.             CIRCLE (mx(1), y1), 2, &HFFFFFF00 'marking intersect points yellow
69.             CIRCLE (mx(1), y2), 2, &HFFFFFF00
70.             CIRCLE (mx(1), y1), 4, &HFFFFFF00 'marking intersect points yellow
71.             CIRCLE (mx(1), y2), 4, &HFFFFFF00
72.  
73.         END IF
74.     ELSE
75.         'OK the calculations!
76.         'from inserting eq ofline into eq of circle where line intersects circle see reference
77.         ' https://math.stackexchange.com/questions/228841/how-do-i-calculate-the-intersections-of-a-straight-line-and-a-circle
78.         A = m ^ 2 + 1
79.         B = 2 * (m * Y0 - m * q - p)
80.         C = q ^ 2 - r ^ 2 + p ^ 2 - 2 * Y0 * q + Y0 ^ 2
81.         D = B ^ 2 - 4 * A * C 'telling part of Quadratic formula = 0 then circle is tangent  or > 0 then 2 intersect points
82.         IF D < 0 THEN ' no intersection
83.             PRINT "m, y0 "; TS$(m); ", "; TS$(Y0)
84.             PRINT "(p, q) "; TS$(p); ", "; TS$(q)
85.             PRINT "A: "; TS$(A)
86.             PRINT "B: "; TS$(B)
87.             PRINT "C: "; TS$(C)
88.             PRINT "D: "; TS$(D); " negative so no intersect."
89.         ELSEIF D = 0 THEN ' one point tangent
90.             x1 = (-B + SQR(D)) / (2 * A)
91.             y1 = m * x1 + Y0
92.             PRINT "Tangent Point Intersect (x1, y1) = "; TS$(x1); ", "; TS$(y1)
93.             CIRCLE (x1, y1), 2, &HFFFFFF00 'yellow circle should be on line perprendicular to 3rd click point
94.             CIRCLE (x1, y1), 4, &HFFFFFF00 'yellow circle should be on line perprendicular to 3rd click point
95.         ELSE
96.             '2 points
97.             x1 = (-B + SQR(D)) / (2 * A): y1 = m * x1 + Y0
98.             x2 = (-B - SQR(D)) / (2 * A): y2 = m * x2 + Y0
99.             PRINT "2 Point intersect (x1, y1) = "; TS$(x1); ", "; TS$(y1); "  (x2, y2) = "; TS$(x2); ", "; TS$(y2)
100.             CIRCLE (x1, y1), 2, &HFFFFFF00 'marking intersect points yellow
101.             CIRCLE (x2, y2), 2, &HFFFFFF00
102.             CIRCLE (x1, y1), 4, &HFFFFFF00 'marking intersect points yellow
103.             CIRCLE (x2, y2), 4, &HFFFFFF00
104.         END IF
105.     END IF
106.     _DISPLAY
107.     INPUT "press enter to continue, any + enter to quit "; q$
108.     IF LEN(q$) THEN SYSTEM
109.     pi = 0 'point index
110. LOOP UNTIL _KEYDOWN(27)
111.  
112. SUB slopeYintersect (X1, Y1, X2, Y2, slope, Yintercept) ' fix for when x1 = x2
113.     slope = (Y2 - Y1) / (X2 - X1)
114.     Yintercept = slope * (0 - X1) + Y1
115. END SUB
116.  
117. FUNCTION TS$ (n)
118.     TS$ = _TRIM$(STR$(n))
119. END FUNCTION