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Intersecting Simple Surfaces

Learn about intersecting simple surfaces, including infinite planes, polygons, convex shapes, and ray shooting. Discover how to determine if a point is inside a polygon and how to test if a point lies inside a given shape using winding number or ray intersection techniques.

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Intersecting Simple Surfaces

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  1. Intersecting Simple Surfaces Dr. Scott Schaefer

  2. Types of Surfaces • Infinite Planes • Polygons • Convex • Ray Shooting • Winding Number • Spheres • Cylinders

  3. Infinite Planes • Defined by a unit normal n and a point o

  4. Infinite Planes • Defined by a unit normal n and a point o

  5. Infinite Planes • Defined by a unit normal n and a point o

  6. Infinite Planes • Defined by a unit normal n and a point o

  7. Infinite Planes • Defined by a unit normal n and a point o

  8. Infinite Planes • Defined by a unit normal n and a point o

  9. Polygons • Intersect infinite plane containing polygon • Determine if point is inside polygon

  10. Polygons • Intersect infinite plane containing polygon • Determine if point is inside polygon • How do we know if a point is inside a polygon?

  11. Point Inside Convex Polygon

  12. Point Inside Convex Polygon • Check if point on same side of all edges

  13. Point Inside Convex Polygon • Check if point on same side of all edges

  14. Point Inside Convex Polygon • Check if point on same side of all edges

  15. Point Inside Convex Polygon • Check if point on same side of all edges

  16. Point Inside Convex Polygon • Check if point on same side of all edges

  17. Point Inside Convex Polygon • Check if point on same side of all edges

  18. Point Inside Convex Polygon • Check if point on same side of all edges

  19. Point Inside Convex Polygon • Check if point on same side of all edges

  20. Point Inside Convex Polygon • Check if point on same side of all edges

  21. Point Inside Convex Polygon • Check if point on same side of all edges

  22. Point Inside Convex Polygon

  23. Point Inside Polygon Test • Given a point, determine if it lies inside a polygon or not

  24. Ray Test • Fire ray from point • Count intersections • Odd = inside polygon • Even = outside polygon

  25. Problems With Rays • Fire ray from point • Count intersections • Odd = inside polygon • Even = outside polygon • Problems • Ray through vertex

  26. Problems With Rays • Fire ray from point • Count intersections • Odd = inside polygon • Even = outside polygon • Problems • Ray through vertex

  27. Problems With Rays • Fire ray from point • Count intersections • Odd = inside polygon • Even = outside polygon • Problems • Ray through vertex • Ray parallel to edge

  28. A Better Way

  29. A Better Way

  30. A Better Way

  31. A Better Way

  32. A Better Way

  33. A Better Way

  34. A Better Way

  35. A Better Way

  36. A Better Way

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  39. A Better Way • One winding = inside

  40. A Better Way

  41. A Better Way

  42. A Better Way

  43. A Better Way

  44. A Better Way

  45. A Better Way

  46. A Better Way

  47. A Better Way

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  49. A Better Way

  50. A Better Way

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