TJ-Bot
I want to create an area. Sounds simple, but if i use the SAT implementation (N-vertices-piligons) i can't make a perfect circle, and i don't want to base it on pixels because its very slow and still not 100%precision. has someone an idea how to do this?
Exact Area in geometry or programming refers to the precise measurement of a shape's surface without approximations like pixel grids or polygonal decompositions. For circles, using only SAT (Separating Axis Theorem)-based polygon approximation means you approximate with many vertices but never truly get a perfect circle, just a polygon with many sides.
To create an exact area for a circle computationally:
- Use the mathematical formula ( \pi r^2 ) instead of polygonal or pixel-based approaches.
- Represent the circle analytically (as equations or functions) rather than as discrete shapes.
- If intersection or collision detection is necessary (like in SAT), combine analytical checks for circles with polygon tests rather than approximating circles as polygons.
SAT is great for convex polygons but not ideal for smooth curves or circles.
For faster operations without pixel-based slowness:
- Use mathematical primitives.
- Use shape-specific algorithms that handle circles exactly.
- Consider using vector math and analytic geometry instead of pixel grids or polygonal approximations.
Useful links:
rose sierra