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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
https://ray-tracing-conept.blogspot.com/2015/01/ray-sphere-intersection.html
Its a quadratic equation in t which gives us two roots which signifies two intersection point on sphere. We can rewrite the equation as: at^2 …
Ray-Sphere Intersection - nordinz notes
https://sites.google.com/site/nordinznotes/home/ray-tracing/ray-sphere-intersection
A sphere is a ball-like shape that can be immediately recognized. However here, we need to elaborate on the concept in a manner much more precise. We need to represent the concept of a sphere in a mathematical manner. The implicit equation describing a sphere with radius r and center is as follows: A point is on the surface of the sphere if and only if the point satisfies the …
Lecture 14: Ray Sphere Intersection
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.
Kyle Halladay - Ray-Sphere Intersection with Simple Math
http://kylehalladay.com/blog/tutorial/math/2013/12/24/Ray-Sphere-Intersection.html
As the diagram below shows, the first step to finding tc is to create a right angle triangle, using tc, the vector from the sphere’s center to the ray’s origin, and a line (d) from the center to the ray. The first thing we need to find is …
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
graphics - ray tracing with sphere - Stack Overflow
https://stackoverflow.com/questions/20184039/ray-tracing-with-sphere
Then the ray is defined by the parametric equation O + tR. 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.
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
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
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 "
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