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How to check if a ray intersects a circle - Stack Exchange
https://math.stackexchange.com/questions/3894559/how-to-check-if-a-ray-intersects-a-circle#:~:text=r%20%E2%88%97%20is%20the%20minimum%20distance%20between%20the,%E2%88%97%20%3C%20r%20they%20intersect%20at%20two%20points.
How to check if a ray intersects a circle - Stack Exchange
https://math.stackexchange.com/questions/3894559/how-to-check-if-a-ray-intersects-a-circle
3 1 Parametrize the ray as ( x, y) = ( o x, o y) + t ( v x, v y). Substitute that into equation of the circle ( x − c x) 2 + ( y − c y) 2 = r 2, you get a quadratic equation in t. the ray intersect the circle iff the quadratic equation have non-negative roots.
RayTracing - UC Santa Barbara
https://sites.cs.ucsb.edu/~yfwang/courses/cs180/notes/raytracing.pdf
Because we have a root of multiplicity 2, ray intersects circle at one point (i.e., it’s tangent to the circle) We can use discriminant D = b2 - 4ac to quickly determine if a ray intersects a curve or not - if D < 0, imaginary roots; no intersection - if D = 0, double root; ray is tangent - if D > 0, two real roots; ray intersects circle at two points
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: intersection and shading
https://www.cs.cornell.edu/courses/cs4620/2013fa/lectures/03raytracing1.pdf
Ray-triangle intersection • Condition 1: point is on ray • Condition 2: point is on plane • Condition 3: point is on the inside of all three edges • First solve 1&2 (ray–plane intersection) – substitute and solve for t: 10
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 I: Ray-Shape Intersection
http://scroll.stanford.edu/courses/cs348b-03/lectures/rt-apr03.pdf
cs348b Matt Pharr, Spring 2003 • [tmin, tmax) range • Carried along with ray, updated to track closest intersection • Object transformations • Transform the ray origin and direction by the inverse transform • Normalize ray direction vector? • Can make intersection tests faster, but renormalizing after transform is slow Various Details
raytracing - Ray - plane intersection - Stack Overflow
https://stackoverflow.com/questions/26920705/ray-plane-intersection
Find the product s= (nx*ex+ny*ey+nz*ez). If it is zero then there is no intersection. Find the distance of the intersection to the point on the line t= (d- (nx*rx+ny*ry+nz*rz))/s. The intersection point is at c= (rx+ex*t, ry+ey*t, rz+ez*t) Share. Follow this answer to …
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 // …
c++ - How to do ray plane intersection? - Stack Overflow
https://stackoverflow.com/questions/23975555/how-to-do-ray-plane-intersection
The ray-plane intersection occurs when q satisfies the plane equation. Substituting, we have: d = -dot (n, q) = -dot (n, p + t * v) = -dot (n, p) + t * dot (n, v) Rearranging: t = - (dot (n, p) + d) / dot (n, v) This value of t can be used to determine the intersection by plugging it back into p + t*v.
Optical and Ray Tracing Mathematics - arachnoid.com
https://arachnoid.com/OpticalRayTracer_technical/resources/opticalraytracer_technical.pdf
Here is the procedure for locating intersections between a light ray and circles representing lenses: •In the following equations, a line of infinite extent is defined by Cartesian10 locations x 1,y 1 and x 2,y 2, both of which lie on the line of interest. •The specific values of x 1,y 1 and x 2,y 2 are less important than the fact that they lie on the line of interest, defined by the initial ray …
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