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Raytracing: Intersection between a line and a sphere - Norech
https://norech.com/blog/post/raytracing-intersection-between-line-and-sphere#:~:text=Raytracing%3A%20Intersection%20between%20a%20line%20and%20a%20sphere,see%20if%20it%20hit%20and%20where%20it%20hits.
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
First we need to check whether ray is intersection with the sphere or not: determinant = sqrt (b^2 - 4ac) b2 – 4ac < 0 ⇒ No intersection b2 – 4ac …
Raytracing: Intersection between a line and a sphere - Norech
https://norech.com/blog/post/raytracing-intersection-between-line-and-sphere
if delta > 0, our ray will go through our sphere and intersect twice its surface. The result of our equation will give us the distance of the intersections relatively to our start position. near_distance = (-b + sqrt (delta)) / 2 far_distance = (-b - sqrt (delta)) / 2. The near distance is the distance where the ray enters the sphere and far distance is the position where the ray will exit …
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
Ray Tracing (Intersection)
https://www.cs.cornell.edu/courses/cs4620/2015fa/lectures/06rtintersectWeb.pdf
• With 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); bool didhit = s.intersect(ray, 0, +inf) …
Lecture 14: Ray Sphere Intersection - Colorado State University
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.
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;}
Sphere Tracing: A Geometric Method for the Antialiased Ray …
https://graphics.stanford.edu/courses/cs348b-20-spring-content/uploads/hart.pdf
Sphere Tracing: A Geometric Method for the Antialiased Ray Tracing of Implicit Surfaces John C. Hart School of EECS Washington State University Pullman, WA 99164-2752 (509) 335-2343 (509) 335-3818 (fax) [email protected] Abstract Sphere tracing is a new technique for rendering implicitsurfaces using geometric distance.
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 Tracing: Rendering a Triangle (Ray-Triangle …
https://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle/ray-triangle-intersection-geometric-solution
// compute d parameter using equation 2 float d = -N.dotProduct(v0); // compute t (equation 3) t = -(N.dotProduct(orig) + d) / NdotRayDirection; // check if the triangle is in behind the ray if (t 0) return false; // the triangle is behind // compute the intersection point using equation 1 Vec3f P = orig + t * dir; // Step 2: inside-outside test Vec3f C; // vector perpendicular to triangle's plane // …
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