2D Line Normals (or: What's your vector, Victor?)
Author
Hello,
I am having a small bit of trouble with normals to a line in 2D. I have been doing a bit of searching on the subject and I understand what a normal is and how to find them. The only thing that really confuses me is the fact that every resource I have read thus far has only talked about one normal (In one direction). Isn't there two possible normals for a given line segment (one off each side)? How do I know which of these to use? I tried to draw a diagram to figure it out but I came up with four possibilities between the ball and its point of impact; either above or below and either left or right. Is there an easy way to only get the normal for the side on which the ball is approaching? I apologize if this has been covered before but I was unable to find it if it was. Thanks in advance.
-cheers
You're correct, there are 2 different normals to a line in 2D; normals in 2D are dependent on your winding order for vertices. Generally people work with counter-clockwise (CCW) vertices. Thus to achieve the normals given in this image:
Image 1
Going from A-D-C-B in counter-clockwise fashion you would derive this equation:
Now if you applied the equation above to clockwise (CW) vertices, you would obtain the "wrong" normal, as shown in this image:
Image 2
Going from A-B-C-D in clockwise fashion. Thus to achieve "correct" normals from Image 1 while maintaining the use of clockwise vertices, you would need to derive the following equations to go from A-B-C-D:
It all depends on what normal you consider correct in 2D, therefore you must decide for yourself.
Image 1
Going from A-D-C-B in counter-clockwise fashion you would derive this equation:
N.x = V2.y - V1.yN.y = V1.x - V2.xNow if you applied the equation above to clockwise (CW) vertices, you would obtain the "wrong" normal, as shown in this image:
Image 2
Going from A-B-C-D in clockwise fashion. Thus to achieve "correct" normals from Image 1 while maintaining the use of clockwise vertices, you would need to derive the following equations to go from A-B-C-D:
N.x = V1.y - V2.yN.y = V2.x - V1.xIt all depends on what normal you consider correct in 2D, therefore you must decide for yourself.
Author
Ah, I see. How would I find the normal that is on the same side of the line as my ball? I was thinking just checking the sign of the difference between the X and Y components but that leaves me with six possibilities and only two vectors to consider. There must be an easier way to do it, or at least a more elegant method. Thanks again.
-cheers
-cheers
Find the dot product of a normal and the vector from either of the line's endpoints to the ball's position. If the result is negative, negate the normal.
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