Ray Tracing Basics

Flashcards covering the basics of ray tracing, including definitions, equations, and concepts related to ray-sphere intersections, illumination models, recursive techniques, and bounding volumes.

What is ray tracing?

Ray tracing is a method for producing realistic images from 3D models by tracing rays through each pixel into the scene and computing the color based on intersections and material properties.

What is a right-handed coordinate system?

A right-handed coordinate system is a 3D coordinate system where the x, y, and z axes are oriented such that if you point your right thumb along the x-axis, your index finger along the y-axis, and your middle finger along the z-axis, the orientation matches the coordinate system.

What is the view reference point (VRP)?

The view reference point (VRP) is a 3D coordinate defining the position of the center of the image plane.

Why is the VRP important?

The VRP is important because it defines the central pixel's position in the image plane, and all other pixels are calculated relative to this point.

What is the view up vector (VUV)?

The view up vector (VUV) is a 3D vector defining the up direction (or y-axis) of the camera in world space.

Why is the VUV important?

The VUV is important because it helps define the orientation of the camera in the world space, ensuring the image is correctly aligned.

What is the ray equation?

The ray equation is p = o + td, where o is the origin of the ray, d is the direction vector, and t is a scalar.

What is the sphere equation?

The sphere equation is (p − cs)² = r², where cs is the center of the sphere and r is the radius.

How do you solve for the intersection point p between a ray and a sphere?

Substitute the ray equation into the sphere equation and solve the resulting quadratic equation for t.

Why do we solve for t in the ray-sphere intersection?

We solve for t to find the distance along the ray where it intersects the sphere, which helps determine the exact point of intersection.

What is the Phong reflection model?

The Phong reflection model is IPixel,c=Ka,cILight,c+Kd,cILight,cn^⋅l^+Ks,cILight,c(r^⋅e^)η.

What does the Phong reflection model account for?

The Phong reflection model accounts for ambient, diffuse, and specular lighting contributions to the final pixel color.

What is the ambient term in the Phong model?

The ambient term is IPixel,c=Ka,cILight,c, representing the light that is uniformly present in the scene.

Why is the ambient term important?

The ambient term is important because it simulates indirect lighting, providing a baseline level of illumination that prevents objects from appearing too dark.

What is the diffuse term in the Phong model?

The diffuse term is IPixel,c=Kd,cILight,c n^⋅l^, representing the light that scatters in many directions from the surface.

Why is the diffuse term important?

The diffuse term is important because it simulates how light interacts with matte surfaces, providing realistic shading based on the angle between the light source and the surface normal.

What is the specular term in the Phong model?

The specular term is IPixel,c=Ks,cILight,c(r^⋅e^)η, representing the light that reflects off the surface in a mirror-like manner.

Why is the specular term important?

The specular term is important because it simulates highlights and reflections, giving objects a shiny appearance.

What is recursive ray tracing?

Recursive ray tracing is a technique that extends ray tracing by tracing additional rays for effects like reflection, refraction, and shadows.

Why is recursive ray tracing used?

Recursive ray tracing is used to achieve more realistic rendering by simulating complex light interactions such as reflections and refractions.

What is the equation for combining reflected colors in recursive ray tracing?

The combined color is C=kreflCp+(1−krefl)Cs, where krefl is the reflectivity of the object.

Why do we use the reflectivity coefficient krefl in recursive ray tracing?

The reflectivity coefficient krefl is used to determine how much of the reflected light contributes to the final color, allowing for realistic simulation of reflective surfaces.

What is a bounding volume?

A bounding volume is a simple shape (like a box or sphere) that encloses an object, used to quickly determine if a ray might intersect the object.

Why are bounding volumes used in ray tracing?

Bounding volumes are used to reduce the number of intersection tests, improving the efficiency of ray tracing by quickly eliminating large areas of the scene that do not need detailed testing.

What is a bounding volume hierarchy (BVH)?

A bounding volume hierarchy (BVH) is a tree structure where each node represents a bounding volume containing a subset of the scene's objects, used to efficiently query intersections.

Why is a BVH used in ray tracing?

A BVH is used to achieve efficient ray tracing by hierarchically subdividing the scene, allowing rays to be tested against fewer objects and reducing the overall computational cost.

What is the time complexity of querying a BVH with a ray?

The time complexity of querying a BVH with a ray is O(logn) per ray, leading to O(mlogn) for m rays.

Why is the O(logn) query time important for BVHs?

The O(logn) query time is important because it allows for efficient ray tracing even with large scenes, enabling real-time rendering and faster image generation.