Ray tracing in computer graphics Ray tracing Figure

Ray tracing in computer graphics

Ray tracing Figure 3. Tracing rays from the light source to the eye. Lots of rays are wasted because they never reach the eye. Figure 4. We trace a new ray from each ray-object intersection directly towards the light source

Reflection and refraction Figure 6. Recursive reflection and refraction

Ray tracing in computer graphics

Scattering from a patch : Green’s theorem where

Physical optics approximation where Incident wave where reflect wave

Scattered wave from a patch Receiver position Source position Equi-phase plane

Radiation pattern vs. patch size

The Basic Idea • Simulate light rays from light source to eye Light Eye R t eflec Incid ay r d e ent r Surface ay

“Forward” Ray-Tracing • Trace rays from light • Lots of work for little return Light Image Plane Light Rays Eye Object

“Backward” Ray-Tracing • Trace rays from eye instead • Do work where it matters Light Image Plane Eye Object This is what most people mean by “ray tracing”.

Backward ray tracing

Generating Rays • Trace a ray for each pixel in the image plane tan(fovx) * 2 Image Plane fovx Eye (Looking down from the top)

Generating Rays n Trace a ray for each pixel in the image plane (Looking from the side) m (tan(fovx)* 2) / m Eye n Image Plane (tan(fovy)* 2) / n

Triangle Intersection n n Want to know: at what point (p) does ray intersect triangle? Compute lighting, reflected rays, shadowing from that point x ? ? ?

Triangle Intersection • Step 1 : Intersect with plane Plane normal n = <A, B, C> p rd ro p = -(n. ro + D) / (n. rd )

Triangle Intersection n Step 2 : Check against triangle edges n V 1 V 0 V 1 E 0 p V 0 Ei = Vi. Vi+1 x n (plane A, B, C) di = -A. N (plane D) V 2 Plug p into (p. Ei + di ) for each edge if signs are all positive or negative, point is inside triangle!

Generating Rays n Trace a ray for each pixel in the image plane render. Image(){ for each pixel i, j in the image ray. set. Start(0, 0, 0); // ro ray. set. Dir ((. 5 + i) * tan(fovx)* 2 / m, (. 5 + j) * tan(fovy)* 2 / n, 1. 0); // rd ray. normalize(); image[i][j] = ray. Trace(ray); }

Ray tracer • Recursive ray evaluation ray. Trace(ray) { if (n>N) return ray. Efield; obj = hit. Object(ray, p, n, triangle); if (!obj)return black; if(obj->material==reflective) { ray. reflect(); n++; ray. Trace(ray); } if (obj->material==transmissive) { ray. transmit(); n++; ray. Trace(ray); } }

Acceleration • 1280 x 1024 image with 10 rays/pixel • 1000 objects (triangle, CSG, NURBS) • 3 levels recursion 39321600000 intersection tests 100000 tests/second -> 109 days! Must use an acceleration method!

Bounding volumes • Use simple shape for quick test, keep a hierarchy

Space Subdivision • Break your space into pieces • Search the structure linearly

Reciprocity Transmitting mode Receiving mode 수신 안테나 송신 안테나 수신 안테나

Projection screen

Calculation of E-field 투과 및 반사계수 (dyadic)

Fields and power radiated by an antenna In the far field, : Poynting vector (power density) If the transmitted power is PT,

Antenna pattern characteristics E-plane, H-plane

Directivity : D

Antenna gain and efficiency : Gain takes into account losses and reflections of the antenna. Antenna gain and effective area Received power : Radiation power density by a transmitting antenna

Radar cross section 31 Pt : 송신 전력 Transmit Receive : Power received by an obstacle with cross section σ : Reradiated power density by the obstacle : Received power due to scattering

Return signal modeling by RCS 32

RCS 측정 setup 33

RCS 측정 34 Maximum 29 m

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