MATLAB: 2-D Ray Tracing

2dplottingray trace

Hi everyone, I have been tackling a problem in regards to ray tracing in 2-dimensions and havent been able to find anything helpful to help me start the program I want. My goal is to be able to plot a ray in a confined space that reflects the ray, but each time it hits a wall the ray decays a little until it vanishes eventually. I've been able to plot a ray and a "wall", but making the actual reflecting line is what's troubling me. I have found the point of intersection of 2 lines, and the angle I want the reflection to come out at (supw1). Any help to this problem is greatly appreciated, I essentially want to be able to make the ray "laser" bounce around like the old fashioned DVD logo from back in the day. Attached is the Matlab code I have so far. Thanks in advanced for the help, feel free if you have any questions for clarification.
%line1
x1 = [2 3];
y1 = [1 1];
%line2
x2 = [2 10];
y2 = [0 10];
%fit linear polynomial
p1 = polyfit(x1,y1,1);
p2 = polyfit(x2,y2,1);
% p3 = polyfit(x3,y3,1);
% calculate intersection
x_intersect = fzero(@(x) polyval(p1-p2,x),3);
y_intersect = polyval(p1,x_intersect);
% function drawLine(point,slope)
% % point - vector [x,y]
% % slope - slope of the line
% 




% x = x_intersect;
% y = y_intersect;
% 
% lengthLine = 5;
% 
% xLine = x-lengthLine:x+lengthLine;
% yLine = slope*(xLine-x) + y;
% 
% plot(x,y,'ro')
% plot(xLine,yLine,'b')
% 
% end
intlines = 1;
% if intlines == 1
%     plot(
line(x1,y1);
hold on;
line(x2,y2);
plot(x_intersect,y_intersect, 'ro', 'Markersize', 18)
rectangle('Position',[1 1 11 11])
diff = (atan((y1(2)-y1(1))/(x1(2)-x1(1))) - atan((y2(2)-y2(1))/(x2(2)-x2(1)))) * 180/pi;
supw1 = abs(diff / 2);

Best Answer

Let P1=[x1,y1] and P2=[x2,y2] be the two endpoints of a line segment of the reflecting "wall", and let P3 = [x3,y3] be a point on a ray with vector v = [v1,v2] pointing from P3 along the ray. Assume that the ray will intersect the given line segment. The point of intersection, P4, of the ray with the wall segment will be:
t = ((y2-y3)*v1-(x2-x3)*v2)/((x1-x2)*v2-(y1-y2)*v1);
P4 = t*P1+(1-t)*P2;
[Note #1: If t lies outside the interval [0,1], then the ray doesn't actually intersect the segment.]
The point, P5, at the mirror image of P3 with respect to the line perpendicular to the segment at P4 will be:
P5 = P3+2*dot(P4-P3,P2-P1)/dot(P2-P1,P2-P1)*(P2-P1);
Thus, the reflected ray proceeds from P4 and goes through P5.
[Note #2: This just gives the direction of the reflected ray from P4 toward P5. It doesn't matter if P5 lies outside the other parts of your "wall".]
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