Finder what point is to the left of a line/point after spinning it

Question

I am currently trying to write a shader in unity that draws a triangular pattern around countries in a risk-styled game if both countries are not owned by the same player (v

Answer 1

1. which way is left/right on a line?

   From last edit is this not your case. Why not use dot product?

   

   So if the line goes in -x direction the result is negative and if in the +x direction then the result is positive. if the result is zero that means the line goes up or down only or it is juts a point. If you need specific direction instead of left/right then use appropriate a vector instead of x axis.

   • dot(a,b)=a.x*b.x+a.y*b.y in 2D
   • dot(a,b)=a.x*b.x+a.y*b.y+a.z*b.z in 3D

   Image is relevant for cases where a vector is in unit size in that case the result of dot is perpendicular projection of b into a just like on image

2. on which side is some point?

   I think this is what you need.

   

   As you can see if you handle line (P0,P1) and point P you want to classify as triangle then its polygon winding determines also the side of the line. So for implicit axis directions:

   • CW(clockwise) polygon winding means right side of the line
   • CCW(counter-clockwise) polygon winding means left side of the line

   How to get winding? ... simply compute normal vector and get its Z coordinate. Its polarity (sign) determines winding (CW/CCW or the other way around depends on the coordinate system).

   • normal vector is computed as cross product of the two vertices of triangle (P1-P0)x(P-P1)

   No need to compute other axises just the z so:

   • normal.z = ((P1.x-P0.x)*(P.y-P1.y)) - ((P1.y-P0.y)*(P.x-P1.x))

   Now just do if (normal.z<0) ... else ... it should never be zero unless you call it for point on the line or the line is a point ... look here at similar question: Determine rotation direction /toward/ variable point on a circle