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3 gru 2020 · In the diagram, $q_1$ must be in the blue region for the rays to intersect. We can express one side of the wedge by saying that $q_1$ must be on the same side of the $q_0$ to $p_0$ line as $p_1$ is.
In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedron are vertices.
Intersection against many shapes. The basic idea is: Group.intersect (ray, tMin, tMax) { tBest = +inf; firstSurface = null; for surface in surfaceList { hitSurface, t = surface.intersect(ray, tMin, tBest); if hitSurface is not null { tBest = t; firstSurface = hitSurface; } } return hitSurface, tBest; }
Three ideas about light. Light rays travel in straight lines (mostly) Light rays do not interfere with each other if they cross (light is invisible!) Light rays travel from the light sources to the eye (but the physics is invariant under path reversal - reciprocity).
Ray-triangle intersection. Condition 1: point is on ray. Condition 2: point is on plane. Condition 3: point is on the inside of all three edges. First solve 1&2 (ray–plane intersection) substitute and solve for t:
First consider the math of the ray-plane intersection: In general one intersects the parametric form of the ray, with the implicit form of the geometry. So given a ray of the form x = a * t + a0, y = b * t + b0, z = c * t + c0; and a plane of the form: A x * B y * C z + D = 0;
Intersecting Quadrilaterals • Solving a ray-plane equation determines if the ray hits the polygon plane. It is followed by an extent check to see if the ray hits the polygon. • Let’s write the ray equation as: P = P 0 + D t which defines a ray as: P 0 = ( x 0 , y 0 ,z 0 ) T D = ( d x, d y, d z) T
