Lecture 13/14 Geometric Modeling

Question 1

What are the three most common types of Geometric models?

Answer 1

1. Solid - implicit
2. Surface - parametric
3. Voxel - explicit

Question 2

How does solid modeling work?

Answer 2

Uses sets of points / “chunks” of 3D space.

Question 3

When Rendering Solid Models, what is the ray casting process?

Answer 3

Question 4

What are the surface model formulas?

Answer 4

Question 5

Why are triangle meshes useful for surface texturing?

Answer 5

Triangle meshes are very common

Simplicity and generality: just a set of triangles (vertices + faces)

Efficiently rendered by graphics hardware (three vertices on a plane)

Output of most 3D acquisition tools (3D scanners)

Question 6

What are some methods of Surface Model Rendering

Answer 6

Scan Conversion (this unit)
Ray Tracing
Radiosity
Photon-mapping

Question 7

What are the pros and cons of Scan Conversion (this unit) as a method of surface model rendering?

Answer 7

+ Fast
- Limited realism

Question 8

What are the pros and cons of Ray Tracing

Answer 8

+ Realistic
- Slower
-/+ Leaves a glossy finish

Question 9

What are the pros and cons of Radiosity

Answer 9

+ Models ambient light very well
- Slower

Question 10

What is photon-mapping?

Answer 10

Modern method – combines ray-tracing and radiosity

Question 11

What are voxels?

Answer 11

Voxels are “3D” pixels – cubes, not squares

• f(x,y,z) = some value, possibly a vector of values , (eg. rgb)
• Used for modelling, (3D) textures
• Volume rendering (or fit a surface)

Question 12

What are particle models?

Answer 12

A bunch of “points”
- But the points be any shape
…flocks of birds (boids)
- Fireworks
- Can be used for quick ad-hoc rendering

Question 13

What is Model acquisition?

Answer 13

The process of getting geometric models into a computer

… this can be done by sensors and scanning

Question 14

What are the benefits of using meshes?

Answer 14

Easy to display
…e.g. looping over vertices for fast drawing

Easy to access (instant access to neighbours)
…given a triangle, what are the adjacent triangles?
…given an edge, which two triangles share it?
…given a vertex, which faces/edges share it?

Easy to edit (add/delete vertices, faces)

Question 15

What is needed from a data structure for a mesh?

Answer 15

What we need from data structure:

Representation for faces, edge, vertex and their relationship

Question 16

What is the Face-vertex data structure?

Answer 16

Question 17

What are the pros and cons of a Face-edge-vertex data structure?

Answer 17

+ Store all relationships between faces, vertices and edges

+ Complete representation(everything easily accessible)

• But over-represents information(stores highly redundant information)

Question 18

What is the graphics pipeline?

Answer 18

Question 19

What are the details of stage 1 of the graphics pipeline?

Answer 19

Stage 1: Vertex processing

-Applies transformation from object space to clip (camera) space

• Input: vertex data(position, normal, colour etc.)
• Output: transformed vertices (homogeneous), colours etc.
• Pass along material and shading data (to fragment processing)

Question 20

What are the details of stage 2 of the graphics pipeline?

Answer 20

Stage 2: Clipping and rasterisation

• Turns sets of vertices into primitives and fills them in
• Input: vertices in clip (camera) space, colours, etc.
• Output: set of fragments with interpolated data (3D positions, depth, normals etc.)

Question 21

How can a vertex normal be obtained?

Answer 21

Question 22

What are the details of stage 3 of the graphics pipeline?

Answer 22

Stage 3: Fragment processing

Compute final fragment colours and depth
- Depth often untouched
- Lots of texture mapping (see later)
- Final lighting computations (see later)

INPUT: fragments w/ interpolated data
OUTPUT: final colour and depth

Question 23

Explain Lighting with flat shading, referencing the triangle normal

Answer 23

Shade using the real normal of the triangle
- Piecewise constant (flat) and faceted look

Question 24

Explain Lighting – Gouraud shading, referencing the triangle normal

Answer 24

Compute shading at vertex position, using vertex normals
- Interpolate colours smoothly over the triangle

Question 25

Explain Lighting – Phong shading, referencing the triangle normal

Answer 25

Interpolate normals per pixel, then compute shading - Much better highlights than Gouraud shading (left - right: flat, gourad, phong)

Question 26

Explain stage 4 of the graphics pipeline

Answer 26

Stage 4: Framebuffer processing Hidden surface elimination: - Decides which surfaces are visible framebuffer blending: - Compose transparent surfaces(if necessary) INPUT: fragment colours & depth OUTPUT: final image

Question 27

Explain Hidden Surface Removal (Painter's Algorithm)

Answer 27

Draw objects from back to front, ‘overpainting’ the framebuffer - Simplest way to handle hidden surfaces - May do a lot of useless work (overpainting hidden surfaces) - Not all surfaces can be sorted !

Question 28

Explain the purpose of the z-buffer

Answer 28

Question 29

Explain the process of Hidden Surface Removal: The z-buffer

Answer 29

draw in any order and keep track of closest object allocate depth (z) buffer to store closest depth so far for each pixel when drawing an object, compare its depth to depth buffer value: if less (new object is closer): update both colour framebuffer and depth buffer if greater (new object is occluded): discard object

Question 30

finish stage 2 flashcards ... slide 16 - 21

Question 31

When testing each end point against all frustrum planes, when is the line rejected?

Answer 31

4. Both endpoints are outside and no crossing, reject the line.

Question 32

When testing each end point against all frustrum planes, when is the line fully accepted?

Answer 32

1. Both end points are inside, accept the whole line,

Question 33

When testing each end point against all frustrum planes, when is the line clipped?

Answer 33

2. One end point inside, other outside, clip the line, 3. Both outside but line crosses frustrum, clip the line,

Question 34

When clipping objects (stage 2), when are objects culled?

Answer 34

Full objects are removed (culled) when not in view of frustum (behind the eye). These invisible primitives are removed for efficiency, as they skip later pipeline stages.

Question 35

What is point-plane clipping:

Answer 35

positive dot n * u > 0 product means on the “outside” Test against all 6 frustrum planes.

Question 36

What is Polygon clipping?

Answer 36

Convex polygons are similar to line clipping: Clip each point in sequence - Remove outside points - Create new points on boundary

Question 37

During the rasterization process, what are the two ways to decide which pixels to 'turn on'?

Answer 37

1. Aliased Boundry: pixel is either in the primitive or not. 2. Anti-aliasing... smoothing

Question 38

What does the rasterization step do in the graphics pipeline?

Answer 38

Approximates primitives into pixels(centred at integer coordinates)

Question 39

What are the steps of rasterization?

Answer 39

1. Determine which pixels to turn on: Input: vertex position in homogeneous coordinates 2. interpolate values across primitive e.g. colour, normals, position, depth at vertices Input: any vertex property

Question 40

If two triangles overlap, which dominates the pixel during triangle rasterization?

Answer 40

Triangle rasterization: Scan Conversion The pixel covering the pixel center dominates