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Ray Tracing: Ray Sphere Intersection
https://ray-tracing-conept.blogspot.com/2015/01/ray-sphere-intersection.html
Ray Tracing: intersection and shading
https://www.cs.cornell.edu/courses/cs4620/2013fa/lectures/03raytracing1.pdf
Ray-sphere intersection: algebraic • Condition 1: point is on ray • Condition 2: point is on sphere – assume unit sphere; see Shirley or notes for general • Substitute: – this is a quadratic equation in t 4
Raytracing: Intersection between a line and a sphere - Norech
https://norech.com/blog/post/raytracing-intersection-between-line-and-sphere
Raytracing: Intersection between a line and a sphere Raytracing is a way to precisely compute how the light will hit an object. It consists of sending a ray to an object (imagine a sort of laser) and see if it hit and where it hits. At the era of RTX cards, this word might seem quite familiar.
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 (Intersection)
https://www.cs.cornell.edu/courses/cs4620/2015fa/lectures/06rtintersectWeb.pdf
Ray intersection in software • Scenes usually have many objects • Need to find the first intersection along the ray – that is, the one with the smallest positive t value • Loop over objects – ignore those that don’t intersect – keep track of the closest seen so far – Convenient to give rays an ending t value for this purpose (then
Lecture 14: Ray Sphere Intersection
https://www.cs.colostate.edu/~cs410/yr2017fa/more_progress/pdfs/cs410_F17_Lecture10_Ray_Sphere.pdf
Lecture 14: Ray Sphere Intersection September 21, 2017 Sphere Intersection •Sphere centered at Pc with radius r. 9/21/17 CSU CS 410 Fall 2017 ©Ross Beveridge & Bruce Draper P−P c 2=r2 L+sU−P c 2−r2=0 substitute T=P c −L Yieldingaquadraticequation (sU−T)⋅(sU−T)−r2=0 L 2 Brute Force (II) •Expand to see what is happening.
Ray Tracing I: Ray-Shape Intersection
http://scroll.stanford.edu/courses/cs348b-03/lectures/rt-apr03.pdf
Classic Ray Tracing. ... • Found a valid intersection Ray-Plane Intersection r(t) = O + t ! D (P ! P ) á N = 0 t ! [tmin, tmax) cs348b Matt Pharr, Spring 2003 ... • 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 "
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:
Kyle Halladay - Ray-Sphere Intersection with Simple Math
http://kylehalladay.com/blog/tutorial/math/2013/12/24/Ray-Sphere-Intersection.html
If the result of this is that tc is less than 0, it means that the ray does not intersect the sphere, and we can bail out of our intersection test early. If it’s not less than 0, we move on. The last thing we need to do with this triangle is solve for the length of d.
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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