3D Pipeline

Question 1

Points in 3D space are represented by…

Answer 1

Three coordinates: length, width and depth, or x, y and z.

Question 2

Linear transformations are encoded as…

Answer 2

3 x 3 matrices

Question 3

Homogeneous coordinates are used for affine transformations, resulting in vectors of shape […] and matrices of shape […].

Answer 3

4-dimensional homogeneous vectors and 4 x 4 matrices

Question 4

Scaling and translation are the same as in 2D, however […] is not. (pick 1)

Answer 4

Rotation, shearing

Question 5

Rotation is a different process than in 2D because…

Answer 5

In 2D, we rotate around the origin of the coordinate system, however in 3D we rotate around a chosen axis

Question 6

The inverse of a rotation is denoted mathematically as R^-1, but since rotation matrices are orthogonal, it may also be given as…

Answer 6

The transpose of the original matrix

Question 7

Any 3D rotation can be expressed as a sequence of…

Answer 7

Three rotations around the main axes

Question 8

In order to rotate a vector v around a non-global axis, we need to begin by first… (HINT: similar to rotation around a point)

Answer 8

Aligning v to one of the coordinate system’s main axes, to be reversed later

Question 9

We can use Euler-Rodrigues to calculate the matrix for a rotation given an axis u such that u is… (HINT: Vector3.forward is [0, 0, 1])

Answer 9

The axis u is a unit vector

Question 10

Given an affine transformation A, a normal of a 3D object n must be calculated as…

Answer 10

The inverse of the transpose of A multiplied by n, or (A^T)^-1 n

Question 11

In order to convert nD coordinates to mD, we use a type of geometry called…

Answer 11

Projective geometry

Question 12

When converting from 3D to 2D, we map points from 3D space to a…

Answer 12

Projection plane

Question 13

Where the camera exists and is pointing is called…

Answer 13

The Centre of Projection

Question 14

The projection plane is a…

Answer 14

Plane which contains 3D world points mapped to a 2D local space

Question 15

The rendering pipeline stage contains steps such as… (pick 3)

Answer 15

Shading, transformation, lighting, rasterization (pick 3)

Question 16

Normals are…

Answer 16

The point at which each face on a model is facing

Question 17

Normals are used for… (pick 2)

Answer 17

Anything related to viewer-facing improvements.

Bump/displacement mapping, lighting, surface smoothing, subsurface divisions (pick 2) (don’t use subsurface divisions as a mental example, it’s too complicated)

Question 18

The 3D pipeline transforms 3D objects by […] vertices onto a […].

Answer 18

Projecting vertices onto a screen.

Question 19

After projecting vertices onto a screen, the 3D pipeline then handles…

Answer 19

Lighting and shading.

Question 20

The final step of the 3D pipeline is… (HINT: to be output to the LED screen)

Answer 20

Rasterisation

Question 21

The two types of projection are…

Answer 21

Perspective and parallel.

Question 22

While perspective projection uses projection lines that converge at the center of projection, parallel projection…

Answer 22

Uses projection lines are parallel to each other, projecting objects in 3D space onto a fixed-size projection plane.

Question 23

While parallel projection uses projection lines that are equal to each other, perspective projection…

Answer 23

Uses projection lines that converge at the center of projection, projecting objects onto a plane defined at a chosen point.

Question 24

The distance a parallel projection may cover is…

Answer 24

Infinite, as the lines are parallel

Question 25

In perspective projection, as objects get further away, they appear...

Answer 25

Smaller.

Question 26

While world space represents the overall coordinate system in our scene, view space represents...

Answer 26

The coordinate system of all objects relative to the camera, or center of projection.

Question 27

What is the purpose of the canonical view space?

Answer 27

Canonical view space is a coordinate system that is a copy of view space, except all points are normalised.

Question 28

What is the difference between position and orientation?

Answer 28

Position is a 3D point in world space, while orientation is where the camera is pointing, represented as a 3D normal.

Question 29

Instead of defining a Center of Projection for an orthographic projection, we instead define...

Answer 29

A Direction of Projection (DOP)

Question 30

All x, y and z components in an orthographic view space are [...] mapped to normalised device coordinates.

Answer 30

Linearly

Question 31

The pinhole camera model represents...

Answer 31

A box with a small aperture on one side, and a light sensitive surface on the other

Question 32

The focal length in a perspective projection model is...

Answer 32

The distance between the center of projection and the plane of projection

Question 33

In perspective projection, a 3D point within a truncated pyramid frustum is mapped to...

Answer 33

The canonical view space

Question 34

Near and far clipping distances in frustum projection refer to...

Answer 34

How far an object needs to be from the camera to be seen, and the maximum object distance respectively

Question 35

Defining the field of view generates the left and right [...] planes.

Answer 35

Clipping

Question 36

Viewport transformation describes the process of...

Answer 36

Converting the normalised distance values (canonical) to viewport pixel coordinates

Question 37

To transform from local to world space, we use a [...] matrix.

Answer 37

Model matrix

Question 38

To transform from world to view space, we use a [...] matrix.

Answer 38

View matrix

Question 39

To transform from view to clip space, we use a [...] matrix. (HINT: we use frustums for this)

Answer 39

Projection matrix

Question 40

To transform from clip space to screen space, we use a...

Answer 40

Viewport transformation

Question 41

Local coordinates are the coordinates of each [...], while global coordinates consist only of the [...] of this local primitive.

Answer 41

Vertex, position (and orientation)

Question 42

MIP mapping is good for... (pick 2)

Answer 42

Better texture quality at distance, better performance, prevention of texture popping artefacts

Question 43

The goal of texture mapping is to map a [...] onto a [...].

Answer 43

2D image onto a 3D object.

Question 44

In OpenGL, textures are stored as images, and each pixel is also called a...

Answer 44

Texture element, or texel

Question 45

Each vertex of the mesh is associated with a [...] on the texture.

Answer 45

Normalised point

Question 46

A texture atlas, also known as a sprite, is...

Answer 46

An image containing multiple smaller images, typically packed together to reduce dimensions

Question 47

Pelting is a technique used to map textures onto [...], by [...].

Answer 47

Complex, organic shapes, by flattening the model's surface into a 2D plane

Question 48

To map a texture to the screen, we use...

Answer 48

Forward mapping

Question 49

To map the screen to a texture coordinate, we use...

Answer 49

Inverse mapping

Question 50

The benefit of using inverse instead of forward mapping for texture rendering is...

Answer 50

Inverse mapping allows us to only render what is being displayed on screen, rather than rendering the whole object's texture

Question 51

At the rendering step, each fragment's texture coordinates are interpolated from...

Answer 51

The triangle it belongs to

Question 52

When interpolating texture coordinates, we often find ourselves between texels. To solve this, we can choose either...

Answer 52

The nearest texel, or a weighted average of the neighbours.

Question 53

Environment mapping represents the distant 'environment' as...

Answer 53

A texture, usually a cube or sphere

Question 54

Sphere mapping maps the environment onto...

Answer 54

A distant sphere surrounding the scene

Question 55

Cube mapping maps the environment onto...

Answer 55

The six faces of a distant cube

Question 56

Cube mapping and sphere mapping is performed using...

Answer 56

A framebuffer

Question 57

In OpenGL, textures have their own texture binding, called...

Answer 57

GL_TEXTURE1 or GL_TEXTURE2D

Question 58

In OpenGL, cube maps have their own texture binding, called...

Answer 58

GL_TEXTURE_CUBE_MAP, alongside _POSITIVE_X, _POSITIVE_Y, and so on

Question 59

We can use the framebuffer to render an image like a cube map without being immediately...

Answer 59

Displayed on screen

Question 60

Bump mapping lets you simulate [...] variations by adjusting the [...] of surface normals.

Answer 60

Height variations, by adjusting the direction of surface normals.

Question 61

A heightmap is a texture provided to the shader that defines, for each pixel on the model...

Answer 61

How high up it should be

Question 62

Bump mapping is typically applied [before/after] shading.

Answer 62

Before

Question 63

The process of shadowing is done to determine...

Answer 63

Volumes created by shadows

Question 64

A shadow volume is represented as a [3D object/2D plane].

Answer 64

3D object

Question 65

A point is considered 'in shadow' if it is within...

Answer 65

The shadow volume

Question 66

To handle situations where multiple shadow volumes influence a single point, we use [...], which increment once for each...

Answer 66

Shadow counters, which increment once for each time the point is in shadow

Question 67

Shadow mapping is the process of creating...

Answer 67

A shadow map texture

Question 68

A shadow map is used as...

Answer 68

A lookup table to determine if the light from a light source is covered by an object or not

Question 69

Shadow mapping may be performed [frame-by-frame/statically/both].

Answer 69

Both - performing it statically is called baking

Question 70

Shadow maps are generated [for each light/for each observer], from [a fixed perspective/its total perspective].

Answer 70

For each light, from its total perspective

Question 71

Shadow maps are generated by using a [view/projection/clip] matrix from the perspective of the light.

Answer 71

Clip matrix

Question 72

Some examples of situations where faces may not be rendered are...

Answer 72

If the face is outside of the frustum, if the face is not facing towards the viewer, or if the face is hidden behind some other object.

Question 73

Culling is a technique that optimises a scene by...

Answer 73

Removing faces that don't need to be rendered due to visibility or other reasons

Question 74

View-Frustum culling is a technique that uses the frustum to...

Answer 74

Remove any objects that fall outside of the camera frustum

Question 75

Clipping is performed in the vertex [post/pre]-processing stage in the rendering pipeline.

Answer 75

Post | It occurs after objects have been projected, but before rasterisation

Question 76

Back-face culling is a technique that culls faces if...

Answer 76

The face is not pointing towards the camera

Question 77

In back-face culling, a face is culled if the dot product of its normal and the vector from the viewpoint is [lesser/greater] than zero.

Answer 77

Greater ## Footnote This value being greater than zero implies the face is rotated 180 degrees from the camera viewpoint

Question 78

Occlusion culling is a technique used when...

Answer 78

Multiple objects or polygons share the same screen coordinates, but have different depths (one object is in front of another)

Question 79

One way to handle occlusion culling is by using Painter's algorithm, where we...

Answer 79

Draw objects from farthest to nearest, and sort these objects by depth

Question 80

One way to handle occlusion culling is by using the Z-Buffer algorithm, where we...

Answer 80

Create a buffer containing the closest known depth in this rendering pass-over, and when we find an object with a closer depth, we update it

Question 81

The Z-Buffer algorithm is a [image-space/object-space] approach, while Painter's algorithm is known as a [image-space/object-space] approach.

Answer 81

Image-space, object-space

Question 82

Z-fighting occurs when two surfaces are...

Answer 82

Very close in depth, causing pixels to alternately be drawn from either surface, resulting in visual artifacts

Question 83

Alpha values are used in rendering transparency to...

Answer 83

Measure the proportion of the transparent object that should be rendered compared to the objects behind it

Question 84

Transparency uses a technique called blending, where we...

Answer 84

Combine colours from multiple layers based on their alpha values