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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) …
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 > 0 ⇒ Two solutions (enter and exit) b2 – 4ac = 0 ⇒ One solution (ray grazes sphere) If the ray intersects the sphere we need to find the smallest root:
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 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
Lecture 14: Ray Sphere Intersection - Colorado State …
https://www.cs.colostate.edu/~cs410/yr2017fa/more_progress/pdfs/cs410_F17_Lecture10_Ray_Sphere.pdf
s=(U⋅T)±(U⋅T)2−T2+r2. 5. Actual Intersection Points. •Compute the two svalues for the two intersections: •Compute the actual positions along the ray for the smallest positive s: 9/21/17 CSU CS 410 Fall 2017 ©Ross Beveridge & Bruce Draper. s. 1.
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 Tracing I: Ray-Shape Intersection
http://scroll.stanford.edu/courses/cs348b-03/lectures/rt-apr03.pdf
• Implicit sphere: • Parametric surface: • 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 "z = r sin ! x = r cos ! cos "! = ! min + v á (! max ! ! min)! = u á ! max
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;}
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: 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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