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INTERSECTING A RAY WITH A QUADRIC SURFACE - ScienceDirect
https://www.sciencedirect.com/science/article/pii/B9780080507552500622#:~:text=Ray%20tracing%20or%20ray%20firing%20is%20also%20a,surfaces%20including%20ellipsoids%2C%20cones%2C%20cylinders%2C%20paraboloids%20and%20hyperboloids.
Ray / Quadric Intersection - University of Washington
http://skuld.bmsc.washington.edu/people/merritt/graphics/quadrics.html
Ray - Quadric Intersection. (Treatment taken from " Practical Ray Tracing in C " by Craig A. Lindley, John Wiley & Sons, 1992, pp. 86-89) The class of quadrics (surfaces that can be defined by a quadratic equation) include cylinders, cones, ellipsoids, paraboloids, etc. Note that spheres and planes are a special subclass but have faster routines as special cases.
Ray-Object Intersection for Planes, Spheres, and Quadrics
https://www.cs.uaf.edu/2012/spring/cs481/section/0/lecture/01_26_ray_intersections.html
Ray-Quadric Intersection Following the usual technique for raytracing, we plug the ray equation P = C + t D into the object's function: f(P) = dot(P,A P) f(C + t D) = dot(C + t D, A (C + t D) ) f(C + t D) = dot(C + t D, A C + t A D ) f(C + t D) = dot(C,AC) + t dot(C,AD) + t dot(D,AC) + t 2 dot(D,AD) This is just a quadratic equation, with coefficients:
Ray / Quadric Intersection - ACM SIGGRAPH
https://education.siggraph.org/static/HyperGraph/raytrace/rtinter4.htm
Ray / Quadric Intersection. (Treatment taken from "Practical Ray Tracing in C" by Craig A. Lindley) The class of quadrics (surfaces that can be defined by a quadratic equation) include cylinders, cones, ellipsoids, paraboloids, etc. Note that spheres and planes are a special subclass but have faster routines as special cases.
Ray Tracing Quadrics - Zoe Wood's CPE 473-01, Winter 2010
http://users.csc.calpoly.edu/~zwood/teaching/csc473/finalw10/mimurray/
Where p + td compose the ray testing the intersection. The intersection points are the results of solving for 't' in A q t 2 + B q t + C q = 0. This can be done by simply using the quadratic formula. To calculate the normal vector for the object, take the partial derivatives of F(x,y,z) (the quadric equation). This turns out to be:
Ray Tracing (Part I)
https://www.cs.purdue.edu/homes/aliaga/cs334-22spring/lectures/lec-raytracing1.pdf
Ray Quadric Intersection •Class of quadrics (surfaces that can be defined by a quadratic equation) include cylinders, cones, ellipsoids, paraboloids, etc •The general quadric surface equation is Ax 2 + By + Cz2 + Dxy+ Exz + Fyz + Gx + Hy + Iz + J = 0 •Substitute the equation of ray, we get the form, A q t2 + B q t + C q = 0
INTERSECTING A RAY WITH A QUADRIC SURFACE
https://www.sciencedirect.com/science/article/pii/B9780080507552500622
Quadric surfaces are common modeling primitives for a variety of computer graphics and computer aided design applications ( Glassner et al., 1989; Blinn, 1984; Gardiner, 1984; Roth, 1982 ). Ray tracing or ray firing is also a popular method used for realistic renderings of quadric surfaces. Summarized in the Gem is an algorithm for locating the intersection point …
Intersection of ray with quadric surface for hobby ray …
https://ompf2.com/viewtopic.php?t=2112
In transform.c++ is code for the usual rotations and translations, as well as concatenating such transforms. In quadric.c++ there are initialization routines for common shapes (sphere, cylinder, cone) and less common shapes (slab, lathe, product of planes). The quadric class also knows how to transform a quadric given an affine transform.
Ray Tracing I: Ray-Shape Intersection
http://scroll.stanford.edu/courses/cs348b-03/lectures/rt-apr03.pdf
Classic Ray Tracing. cs348b Matt Pharr, Spring 2003 ... • Quadric: sphere, cylinder, paraboloid ... • Standard numerical algorithms approaches • Gradient of polynomial gives surface normal at intersection Ray-Algebraic Surface Intersection. cs348b Matt Pharr, Spring 2003
How to set up quadratic equation for a ray/sphere …
https://stackoverflow.com/questions/1986378/how-to-set-up-quadratic-equation-for-a-ray-sphere-intersection
If it is equal to zero, then the ray intersects the sphere at exactly 1 point (it is exactly tangent to the sphere). If it is greater than zero, then the ray intersects the sphere at exactly 2 points. If the discriminant indicates that there's no solution, then you're done! The ray doesn't intersect the sphere.
•Necessary in ray tracing Geometric Queries for Ray …
https://viterbi-web.usc.edu/~jbarbic/cs420-s22/16-geometric-queries/16-geometric-queries-6up.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 10 Ray-Polygon Intersection I • Assume planar polygon in 3D
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