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Raytracing Ray-Ellipsoid Intersect:
http://www.unrouly.com/projects_csgraphics_raytrace.html
Project Overview: Raytracing. Computed two types of intersection for a raytracer, a "Ray-Block" and a "Ray-Ellipsoid". Software: Implemented in C++ in MS Visual Studio. Raytrace Ray-Block Intersection and AABB: I created an AABB by first …
EECS 487: Interactive Computer Graphics
https://web.eecs.umich.edu/~sugih/courses/eecs487/lectures/28-RayTracingImplementation.pdf
Ellipsoid Intersection We have an optimized ray-sphere test • but we want to ray trace an ellipsoid… Let M be a 4× transformation matrix that distorts a sphere (f()) into an ellipsoid For p on ellipsoid, f (M−1p) = 0 f (M−1r t))= e+ d = f (M−1e + t M−1d) Intersection point must be in world coordinates • t is the same in both cases p = e + t d
Ray tracing primitives - University of Cambridge
https://www.cl.cam.ac.uk/teaching/1999/AGraphHCI/SMAG/node2.html
(PDF) Ray tracing in ellipsoidal reflectors for optical ...
https://www.researchgate.net/publication/320533242_Ray_tracing_in_ellipsoidal_reflectors_for_optical_biometry_of_media
the intersection point of the reflected ray with the second ellipsoid focal plane, taking into account the statistical weight of photons. For imaging …
Ray Tracing - Carnegie Mellon University
http://graphics.cs.cmu.edu/nsp/course/15-462/Spring04/slides/13-ray.pdf
Ray-Quadric Intersection • Quadric f(p) = f(x, y, z) = 0, where f is polynomial of order 2 • Sphere, ellipsoid, paraboloid, hyperboloid, cone, cylinder • Closed form solution as for sphere • Important case for modelling in ray tracing • Combine with CSG [see Handout]
Ray / Quadric Intersection - ACM SIGGRAPH
https://education.siggraph.org/static/HyperGraph/raytrace/rtinter4.htm
1. The defining equation for an ellipsoid is as follows: x2/a2 + y2/b2 + z2/c2 = 1 where a, b, and c are the axes for x, y, and z. To displace the ellipsoid from the origin to a position xc, yc, zc, replace x with x - xc, y with y-yc, and z with z …
CS559: Computer Graphics - pages.cs.wisc.edu
http://pages.cs.wisc.edu/~lizhang/courses/cs559-2010s/syllabus/05-03-raytracing2/05-03-raytracing2.pdf
Lecture 28: Ray Tracing Li Zhang. Spring 2010. ... Trace Primary Eye Ray, find intersection Trace Secondary Shadow Ray(s) to all light(s) ... Solution: Ellipsoid transforms sphere Apply inverse transform to ray, use ray-sphere. Acceleration. Testing each object for each ray is slow
Ray Tracing Basics I
http://cs.rit.edu/~jmg/courses/cgII/20072/slides/2-2-raytraceBasics1.pdf
Ray-Sphere Intersection Once we found a ω i for the point of intersection, the actual point is: (x i, y i, z i) = (x 0 + dx * ω i , y 0 + dy * ω, z 0 + dz * ω) The normal at the point of intersection is: (x n, y n, z n) = ((x i - x c)/r, (y i - y c)/r, (z i - z c)/r) (We divide by r to normalize!) Ray-Plane Intersection A plane can be defined by:
Ray - Quadric Intersection
http://skuld.bmsc.washington.edu/people/merritt/graphics/quadrics.html
x 2 /a 2 + y 2 /b 2 + z 2 /c 2 = 1 where a, b, and c are the axes for x, y, and z. To displace the ellipsoid from the origin to a position xc, yc, zc, replace x with x - xc, y with y-yc, and z with z-zc. 2. Put in the actual values for a, b, c, xc, yc, and zc.
Lecture 11 Supplementary note: Ray-Object Intersections
https://cse.hkust.edu.hk/~cktang/csit540-S07/ray-tracing/2-ray-intersection.supp.pdf
ray before testing for intersection. CS341 Computer Graphics Spring Semester 2007 6/17 Intersecting Spheres • The (implicit) equation of a unit sphere is given by: x2 + y 2+ z = 1 • Assuming a unit sphere (radius is equal to one). Substituting the parametric ray equation yields the following: (d xx 0 2 + d yy 0 2 + d zz 0 2) t2 + 2(d x x 0 ...
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