tenta frågor

Question 1

What does the fragment shader do? (Hint: what is its input and output and
when is it executed?)

Answer 1

Receives interpolated values from vertex shader and computes fragment
color. E.g., refines lighting, adds textures, may modify depth

Question 2

What is the z-buffer for?

Answer 2

to resolve visibility / avoid depth sorting.

Question 3

While a normal might be normalized in the vertex shader, why do we generally
need to normalize it again in the fragment shader?

Answer 3

As values get interpolated between the vertices from the vertex shader to
the fragment shader, the interpolated normal in not necessarily normalized.

Question 4

How can you implement fog using the fragment shader?

Answer 4

E.g., (linearly/exponentially) blend between the fragment color and fog
color based on the fragment’s depth. To get full points, draw or explain in more
detail

Question 5

Normally, you would want to draw all geometry that is in front of the camera.
So, why is a near and far plane used for the view frustum?

Answer 5

Near plane is used to avoid a degenerate projection plane. Far plane can be
used to get better z-precision in the z buffer.

Question 6

Describe a test which determines whether or not a sphere and a plane intersect

Answer 6

Insert the sphere center into the plane equation. If the result is smaller than
the radius, there is an intersection.
I.e., ||n•c + d|| <= r.

Question 7

Describe a top-down approach to build an Axis Aligned BSP-tree for a scene.

Answer 7

Create minimal AABB around the whole scene. Split along an axis.
Recursively split the 2 parts alongs a new axis. Terminate if empty node, #triangles
< threshold or level >= max recursion depth. (Axis aligned: x-,y-,z-axis are the split
planes.)

Question 8

Why can’t we use ray tracing to do an exact object-object collision detection
test?

Answer 8

Only tests a discrete subset of surface points and directions. A finite set of
rays may miss small intersections.

Question 9

What is the point of using dynamic collision detection tests?

Answer 9

Objects may collide in space and time although they never collide in any
of the frames rendered at discrete time steps.

Question 10

What is a BRDF? (You can answer by stating what the abreviation BRDF
stands for and assuming f() is a BRDF and describe its input parameters and what it
returns.)

Answer 10

Bidirectional Reflection Distribution Function. The function f(ωi
, ωo)
returns how much of the radiance from the incoming direction ωi
that is reflected in
the outgoing direction ωo.

Question 11

What is caustics?

Answer 11

specular reflections or refractions that focus light

Question 12

Describe the shadow map algorithm

Answer 12

1. Render a shadow (depth) map from the light source.
2. Render image from the eye. For each generated pixel, transform/warp the x,y,zcoordinate to light space and compare the depth with the stored depth value in the
   shadow map (at the pixel position (x,y).
   If greater → point is in shadow.
   Else → point is not in shadow.
   (Bias/offset is necessary due to disretization and precision problems.)

Question 13

Tell which type of curve each image corresponds to. You can choose between
Bezier curve, Interpolation-curve, and Hermite-curve. To get any points, you must
also motivate your choice!

Answer 13

a) interpolation curve since the curve goes through the control points. b)
Hermite-curve since gradients are specified per control point. c) Bezier-curve since
two intermediate points are used to approximate the gradients in the end points.

Question 14

What is direct illumination and what is indirect illumination? (No formulas
needed - words are enough.)

Answer 14

Direct illumination is the light that comes directly from a light source.
Indirect illumination is the inter-reflected light, such as reflections, irradiance,
shadows, caustics, etc.

Question 15

Linear interpolation of (u,v) in screen space does not give perspective correct
texturing. Describe how perspective correct texture interpolation can be achieved.

Answer 15

In screen space, linearly interpolate (u/w, v/w, 1/w) from each vertex.
Then, per pixel: ui
= (u/w)i
/ (1/w)i
, where i means screen space interpolated value.

Question 16

Give two reasons for gamma correction

Answer 16

1) screen output is non-linear so we need gamma to counter that. 2)
Textures/images can be stored with better precision (for human eye) for lowintensity regions.

Question 17

Describe how anisotropic filtering works. Also tell why it is needed

Answer 17

Up to for instance 16 mipmap lookups along the line of anisotropy.
A different amount of filtering in the x and y direction is generally needed.

Question 18

Describe a method for a ray-polygon intersection test. (You may assume that
the polygon is convex and lies in a 3D plane.)

Answer 18

convert to a point-in-2D-polygon test and

use, for instance, the crossing number algorithm / even-odd rule

Question 19

] How do you nicely terminate recursion in ray tracing if you do not simply want
to terminate at a maximum recursion depth?

Answer 19

terminate when the ray’s influence on the final pixel color is below a
certain threshold. (Send a weight with the reflection/refraction rays.)

Question 20

Explain how a skippointer tree works and what the advantage is?

Answer 20

The (BVH)-tree stored in depth first traversal order, sequentially in an
array, with a pointer/index to the next element if traversal of subgraph should be
skipped. Advantage: gives good cache coherence.

Question 21

Explain Final Gather and how it is used with the photon maps. Also, explain
what is good with Final Gather.

Answer 21

Monte Carlo-sample at first bounce using many stochastic rays. (Use
caustics map at first intersection and global+caustics) photon map at intersections of
secondary rays. Good because lowers noise from the global map. (No reduction if
caustics and global map are not specified.)

Question 22

How are soft shadows from an area-light source computed with path tracing?

Answer 22

At each intersection, one shadow ray is shot to one random position on the
light source.

Question 23

Why do you need to use a bias in the shadow map algorithm? What is the cause
of the problem?

Answer 23

We compare two different discretizations - one from the eye and one from
the camera. (To avoid z-fighting (incorrect self shadowing) and light leaking.) The
view sample can lie further from the light than the shadow map sample (due to
discrete sampling).

Question 24

] Consider a game where the model-matrix (the position and orientation) for a car is
described by a translation matrix, T, and a rotation matrix, R, as given below.
1. (1p) When the user presses a key, the car should move 2.0 units in the world-space
x direction. How would you modify the translation matrix?
2. (2p) How would you modify the rotation matrix for the car to turn slightly to the
left?
3. (1p) When the user presses the “up-arrow” key, the car shall move forward in the
direction it is facing. How do you modify the matrices?
4. (1p) We now want a camera from inside the car (at the car’s position and facing in
the rz direction). How can you calculate this matrix?

Answer 24

1. tx = tx + 2
2. You must show that you understand that rz and rx should be rotated around ry
   (E.g., from the labs):
   rz += 0.01 rx
   normalize rz
   rx = rz × ry
3. (tx, ty, tz) += 0.1 rz
   (0.1 is just an example)
4. V = (TR)
   -1

Question 25

[2p] Show how to compute the intersection between a ray and a sphere (in 3D).

Answer 25

Answer: See slides from lecture 6.
Sphere center: c, and radius r
Ray: r(t)=o+td
Sphere formula: ||p-c||=r
Replace p by r(t): ||r(t)-c||=r and solve for t. Return r(t).

Question 26

[3p] Describe how the z-fail algorithm works

Answer 26

Answer: Create shadow quads from the silhouettes of the shadow caster (as seen from
light source). Capping planes are necessary. Render ambient occlusion to color buffer.
Turn off updating of z-buffer and rendering to color buffer. Invert z test, i.e., use
GL_GREATER. Render front facing (as seen from camera) shadow volume polygons to
stencil buffer, decrementing stencil values. Render back facing shadow volume
polygons to stencil buffer, incrementing stencil values. Render diff+spec lighting
contribution to color buffer where stencil buffer = 0

Question 27

[2p] In which ways are NURBS more general than B-Splines?

Answer 27

Answer: control points can be set at non-uniform intervals and they can have different
weights.

Question 28

) [5p] Postprocessing: You have a scene of a spaceship which you render with a shader
called FancyShader, to a texture, OffScreenTexture. To the rendered result, you want to
apply a post-processing effect that generates a gray-scale image.
1. (3p) Order all of the following steps such that you would end up with a grayscale
image of the spaceship in your window:
A. Draw Spaceship
B. Bind GrayScaleShader
C. Draw fullscreen quad
D. Clear rendertarget
E. Bind OffScreenTexture to texture unit 0
F. Bind OffScreenTexture as rendertarget
G. Bind Window (default framebuffer) as rendertarget
H. Bind FancyShader
2. (1p) This is an effect that could instead be implemented directly in FancyShader.
Why could there be a performance advantage of doing it as a post-processing pass
(especially for more computationally heavy effects)?
3. (1p) Most/Many post-processing effects, like blur, can not be implemented in
FancyShader. Why not?

Answer 28

Answer:
1: E.g.: F, D, H, A, G, E, B, C
Actually any of these orders work: ((F → D)/H) → A → (G/E/B) → C, where → means
strict order and / means any order.
2: The performance then scales with pixels, not fragments (or geometry).
3: Need to know result of neighbouring pixels

Question 29

[2p] Which types of filters are common in real-time computer graphics for minification
of 2D textures? (Each listed wrong filter will give negative score. Sum will however not
go below 0p.)

Answer 29

Answer: nearest (box), biliear filtrering (tent) with and without mipmapping. Trilinear
filtering with mipmapping, anisotropic filtering