Angle Reflexion for bouncing ball in a circle

Question

I am making a game with some bouncing elements IN a circle (I use pygame) , My elements have 2 attributes , one for the angle and one for the speed Here is how elements moves :

mvx = math.sin(self.angle) * self.speed  
mvy = -math.cos(self.angle) * self.speed  
self.x += mvx  
self.y += mvy

My problem is this : I know the angle at the top (99.6°) , I have the collision point (x and y ) , but I'm unable to find the angle at the bottom(42.27°) Does someones can make a relation between the first angle and the second ?

Picture is better ...

what about just `a1 = a2 + a3`? `a1 = 42.27 + 28.85*2` – chickity china chinese chicken Feb 05 '19 at 21:31 — chickity china chinese chicken, Feb 05 '19 at 21:31

Rabbid76 · Accepted Answer · 2019-02-06T08:53:39.577

I recommend do calculate the reflection vector to the incident vector on the circular surface.
In the following formula N is the normal vector of the circle, I is the incident vector (the current direction vector of the bouncing ball) and R is the reflection vector (outgoing direction vector of the bouncing ball):

R = I - 2.0 * dot(N, I) * N.

Use the pygame.math.Vector2.

To calculate the normal vector, you' ve to know the "hit" point (dvx, dvy) and the center point of the circle (cptx, cpty):

circN = (pygame.math.Vector2(cptx - px, cpty - py)).normalize()

Calculate the reflection:

vecR = vecI - 2 * circN.dot(vecI) * circN

The new angle can be calculated by math.atan2(y, x):

self.angle  = math.atan2(vecR[1], vecR[0])

Code listing:

import math
import pygame

px = [...] # x coordinate of the "hit" point on the circle
py = [...] # y coordinate of the "hit" point on the circle

cptx = [...] # x coordinate of the center point of the circle
cpty = [...] # y coordinate of the center point of the circle

circN = (pygame.math.Vector2(cptx - px, cpty - py)).normalize()
vecI  = pygame.math.Vector2(math.cos(self.angle), math.sin(self.angle))
vecR  = vecI - 2 * circN.dot(vecI) * circN

self.angle = math.pi + math.atan2(vecR[1], vecR[0])

Thank's a lot ! It works ! I just add PI to the last angle to change his direction self.angle = math.pi + math.atan2(vecR[1], vecR[0]) — Starbuzz6, Feb 06 '19 at 08:49

Hemerson Tacon · Answer 2 · 2019-02-05T21:52:30.873

The inner angles of a triangle need to sum up to 180°. Also, the angle 99.96° is supplementary to the triangle's angle next to it (calling it by A), i.e. 99.96° + A = 180° so A = 180° - 99.96°. Calling of B = 42.27° the bottom angle. And for the last angle C, we can use that it is opposed by the vertex with the other angle that is equal to 2 * 28.85 = 57.7°. Then:

A + B + C = 180°

180° - 99.96° + 42.27°  + 2 * 28.85° = 180°

180° - 99.96° + 42.27°  + 2 * 28.85° = 180°

-99.96° + 42.27°  + 2 * 28.85° = 0°

42.27°  + 2 * 28.85° = 99.96°

B + C = Top angle

P.S.: I know that the values are not exactly equal, but it must be because of the decimal places rounding

Angle Reflexion for bouncing ball in a circle

2 Answers2