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A Minimal Ray-Tracer: Rendering Simple Shapes (Sphere, …
https://www.scratchapixel.com/lessons/3d-basic-rendering/minimal-ray-tracer-rendering-simple-shapes/ray-sphere-intersection
Ray Tracing: Ray Sphere Intersection - Blogger
https://ray-tracing-conept.blogspot.com/2015/01/ray-sphere-intersection.html
c = (e-c). (e-c) - R^2. First we need to check whether ray is intersection with the sphere or not: determinant = sqrt (b^2 - 4ac) b2 – 4ac < 0 …
Ray Tracing: intersection and shading
https://www.cs.cornell.edu/courses/cs4620/2013fa/lectures/03raytracing1.pdf
• With eye ray generation and sphere intersection Surface s = new Sphere((0.0, 0.0, 0.0), 1.0); for 0 <= iy < ny for 0 <= ix < nx {ray = camera.getRay(ix, iy); hitSurface, t = s.intersect(ray, 0, +inf) if hitSurface is not null image.set(ix, iy, white);} 15
Lecture 14: Ray Sphere Intersection - Colorado State …
https://www.cs.colostate.edu/~cs410/yr2017fa/more_progress/pdfs/cs410_F17_Lecture10_Ray_Sphere.pdf
Faster Method -How Fast? •Recall how Ris defined … •Need to compute v… –3 multiplies, 2 additions. •Both r2and c2are already computed. –c2computed for case of ray coming from focal point •Test if r2is greater than (c2-v2) –1 multiply, one conditional. •Only if intersection, Q = E+(v-d)R. –1 subtract, 3 multiplies, 3 additions.
graphics - ray tracing with sphere - Stack Overflow
https://stackoverflow.com/questions/20184039/ray-tracing-with-sphere
Break this into components Ox + tRx, Oy + tRy and Oz + tRz. Substitute these into the equation for the circle x^2 + y^2 + z^2 = 0. This produces a quadratic equation with the variable t. Find the roots of the equation. Now, if you have no real roots, the ray doesn't hit the sphere. If you have one real root then you hit the side of the sphere.
Ray-Sphere Intersection with Simple Math - Kyle Halladay
http://kylehalladay.com/blog/tutorial/math/2013/12/24/Ray-Sphere-Intersection.html
bool intersect (Ray * r, Sphere * s, float * t1, float * t2) {//solve for tc float L = s-> center-r-> origin; float tc = dot (L, r-> direction); if (tc & lt; 0.0) return false; float d2 = (tc * tc)-(L * L); float radius2 = s-> radius * s-> radius; if (d2 > radius2) return false; //solve for t1c float t1c = sqrt (radius2-d2); //solve for intersection points * t1 = tc-t1c; * t2 = tc + t1c; return true;}
Ray Tracing (Intersection)
https://www.cs.cornell.edu/courses/cs4620/2015fa/lectures/06rtintersectWeb.pdf
Intersection against many shapes intersect (ray, tMin, tMax) { tBest = +inf; firstSurface = null; for surface in surfaceList { bool didhit = surface.intersect(hit, ray, tMin, tBest); if didhit { tBest = hit.t; firstSurface = hit.Surface; } } return firstSurface, tBest; } • The basic idea is: – this is linear in the number of shapes
Ray Tracing Basics I - cs.rit.edu
http://cs.rit.edu/~jmg/courses/cgII/20072/slides/2-2-raytraceBasics1.pdf
Most of the computation in ray tracing is determining ray object-intersection When a ray intersects an object, we need to know: Point of intersection Normal of surface at point of intersection Ray-Sphere Intersection The Sphere A sphere can be defined by: Center (x c, y c, z c) Radius r Equation of a point (x s, y s, z s) on a sphere:
Ray Tracing I: Ray-Shape Intersection
http://scroll.stanford.edu/courses/cs348b-03/lectures/rt-apr03.pdf
• Implicit sphere: • Parametric surface: • Parametric sphere: Ray-Sphere Intersection f (x, y, z) = 0 x2 + y2 + z2 ! 1 = 0 f (u, v) = (x, y, z) y = r sin ! cos "z = r sin ! x = r cos ! cos "! = ! min + v á (! max ! ! min)! = u á ! max
Ray Tracing: Rendering a Triangle (Ray-Triangle …
https://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle/ray-triangle-intersection-geometric-solution
The ray can intersect the triangle or miss it. If the ray is parallel to the triangle there is not possible intersection. This situation occurs when the normal of the triangle and the ray direction are perpendicular (and the dot product of these two vectors is 0). We have learned that the dot product of two perpendicular vectors is 0.
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