Babphics Bart Bone

| 14-24: advanced shading stuff | 30-32: mesh and widgets (?) (arcball, mover) | 33-36: bezier curves | 42-45: bezier patches | 55-61: alternative to parametric surfaces

how was rob cook influential

shade trees, cook-torrance lighting model (the pots made of different things)

what does distributed ray-tracing support? (5)

gloss, translucency, penumbra, depth of field, motion blur

what is ray-tracing? what does it NOT have and why is it an issue?

sending out rays through each pixel and seeing what is hit

no pixel-to-pixel coherence, meaning each pixel’s color is completely in isolation from neighbors, unlike rasterization which does interpolation. this is why it is much slower than rasterization!

what is distributed ray tracing

instead of sending out 1 ray per pixel, scatter them around the pixel

(like imagine shooting a point with a sniper rifle vs a shotgun (distributed)

• distributed not just spatially, but in time (e.g. evaluate the rays at different times over 1/24th of a second) and more

what is radiosity?

a global illumination method, where you have light radiate out from the source.

global illumination explanation: the idea that surfaces collect light from more than just a direct light source like the sun or a lightbulb, but from other surfaces reflecting light as well, such as walls, floors, clothes etc., so some surfaces will collect more light than others and thus be lighter

why is rendering equation good

mathematically defines how light bounces off surfaces to simulate global illumination, increases realism!

who came up with the rendering equation

james kajiya

curved shadows on curved surfaces: what is it, who came up with it, how does it work?

1. shadow mapping: if a point can ‘see’ the light sources, it is lit. if it can’t, it’s in shadow

2. by lance williams

3. uses z-buffer: creates a shadow map that records closest possible surface light can hit. later, if u check z buffer and a pixel’s distance is smaller than the stored value in shadow map, it is lit and vice versa.

• basically they used to struggle with shadows on curved stuff it required lots of math, now using shadow mapping and the z values, curved surface and flat work exactly the same since it looks up a single pixel value at a time

does 3d texture increase realism? T/F

true

does subsurface scattering increase realism? T/F

true

general idea of how CAT/MRI/PET scans work? what is the 3d grid made of? what company made like some computer or whatever for this purpose?

1. they go slice by slice, stacked to make a 3d grid made of VOXELS (volume element)

2. semi-transparency decided based on densities (e.g. air is clear, bone is high density should be mostly opaque)

3. ray traced from camera to each pixel through the 3d grid

4. pixar

arcball code info

when the arcball goes down (mouse down/you click), you have a starting quaternion. when you drag, you get a new quaternion and its multipled by start quaternion to get the new orientation.

mover

if you pick a point, you move it in a plane that is perpendicular to the line of sight. the plane updates with your line of sight, ensuring it is always perpendicular and always at the same depth.

• the further red point is the actual point, the closer one is the point being represented on the screen. the plane will always be at the depth of the further red point

name of bezier curve making process

de casteljau construction of bezier curve

how to actually make bezier curve?

• how many control points?

• what is the parameter?

• what is the range of the parameter?

• how to find p?

• what is s?

1. start with 4 control points,

2. t, where you are on the curve

3. 0 to 1, t0 to t1 sweeps out the parametric curve

4. e.g. for p where t = 2/3, go 2/3 along each segment between the control points to get 3 points. connect those 3 points. then go 2/3 along each of those created segments to get 2 points. connect the two points to make one segment. go once more 2/3 along that segment to get the final point p. p is where on the curve you will be when parameter t = 2/3

5. s = 1-t, simplifies the equations significantly

what is a bezier curve with 4 control points called?

a parametric cubic polynomial curve

• one with 3 control points would be called a parametric quadratic polynomial curve

what are the bezier basis functions? what properties do they have (2)?

• they are the coefficients for each of the control points in the equation, made up of s and t

• they form a partition of unity, meaning for any value of t the 4 functions sum up to one.

• the entire curve is contained within the convex hull of the control points (if you stretched a rubber band around the 4 points, curve would always fit within the rubber band)

what is the difference between the B1 and B4 points and the B2 and B3 points?

the bezier curve interpolates (goes through) 1 and 4, but only approximates 2 and 3

does the bezier curve have lots of nice properties

yes

how to ensure continuity between two piecewise bezier curve? what this continuity called

7 points total since they share middle point, middle point (4th) must be halfway between the 3rd and 5th points. c1 continuity

if it not midway, u connected to curve but they dont have c1 continuity

how to make bezier patch?

• how many control points

• what are the two curve called and what are they made of

• how do you find an arbitrary point (u, v) in the patch?

refer to image for #3

1. 16

2. t curve made of s-points, s-curve made of t-points

3. to find e.g. a point (u, v) go up each of the s curves (red lines) until you get the point where s = u. Using these four points (red points), create the t-curve. Find where t = v and yay you have the point you want

given a point u, v with parameters s, t on a bezier patch, how can you find the surface normal? (N(s,t) = ?)

how exact is this answer?

find the tangents of the s curve and the t curve and cross product them together

it is super precise!! it is accurate!! NOT an approximation!!

what key concept does the utah teapot demonstrate??

bezier curves/patches!! can see the control mesh is all straight lines, but turns into a curved shape!

how to split a bezier patch? what happens to the control points?

subdivided into two sub-patches along s-direction (top to bottom down the middle), then split those two patches in the t-direction (left to right horizontally). the result is 1 patch has been split into 4 subpatches

old control points thrown out, new control points have to be calculated

continuity in bezier patches?

same as for curves:

bezier patch boundaries lined up → c0 continuity, position only

tangents/slope line up, control points before and after boundary form a stright line with the boundary points → c1 continuity

alternatives to parametric surfaces (3)

subdivision surfaces, implicit surfaces, particle systems

subdivision surfaces def +

• who came up with them? (2)

• how do they work? (3 steps)

• what do the surfaces become?

blend via recursive smoothing of a polygonal mesh

1. ed catmull, jim clark (silicon graphics guy)

2. e.g. for a rectangle defined by 4 points:

   1. add midpoints on each edge

   2. move each point halfway toward its cw neighbor

   3. repeat

3. surfaces become more smooth with each iteration

implicit surfaces def +

• compare to what?

• how are they different?

• what is the implicit equation for a circle/ what does it mean?

blend via summation of primitives

1. parametric, where you have a single alpha and p = cos alpha, sin alpha

2. parametric: give me parameters, i give you the point
   implicit: give me a test so i can check if a point is on it

3. {p } : px^2 + py^2 − 1 = 0 → set of all p that fit this equation, exact same circle as parametric

   1. if = 0, on circle. positive = outside circle, negative = inside circle

use of implicit surfaces

1. allows you to blend!! see blinn’s blobbies, merging two sphere together. way easier than trying to do it parametrically

2. blue slime blob bob

in implicit surfaces, how do you know where there is an intersection?

if one point is positive and another is negative, you know there MUST be a boundary there somewhere, need to find where it equals 0, repeatedly subdivide and keep testing until you get 0

particle systems def

individual points acting independently, individually displayed

what does this image demonstrate?

cook torrance model

what do these images demonstrate?

distributed ray tracing

what does this image demonstrate?

radiosity

what does this image demonstrate?

radiosity

what is the difference between these two images? one is ___ and one is from __

ray-traced on left, rendering equation on right

what does this image demonstrate?

3d textures

what does this image demonstrate?

subsurface scattering

arcball

bezier patches

what this guys name and nationality (lol)

martin newell, british

patch splitting

what does this show

clark catmull subdivision surfaces

what does this demonstrate

implicit surfaces blending

what does this image demonstrate

implicit surfaces

what does this image demonstrate

particle systems

what is this image showing?

bernstein basis functions for 4 bezier control points