Exam 2021 & 2022

Question 1

Geometry Modelling:
Describe the following types of solid models, mention some advantages or
disadvantages for each (6p)
 Decomposition models

Answer 1

Decomposition models:
 Can be made of:
o Voxels: the solid is composed of a number of cubes
o Cell based: the solid is built up by polygons
 It is an approximate model and requires a lot of memory for high precision.
 It is suitable for different types of calculations

Question 2

Geometry modeling
a) Describe the following types of solid models, mention some advantages or
disadvantages for each (6p)
 Constructive models

Answer 2

Constructive models:
 Solid models are created by manipulating primitives with Boolean operators.
 It is hard to handle general surfaces
 It is very compact (do not require a lot of memory)

Question 3

Geometry modeling
a) Describe the following types of solid models, mention some advantages or
disadvantages for each (6p)
 Boundary representation

Answer 3

Boundary representation:
 The solid is defined with points, curves and surfaces plus a definition of what is inside the
model
 Uses graphical methods e.g. sweep and rotate
 Can use parametric surfaces
 Can use Boolean methods

Question 4

Geometry modelling:
What are half spaces and how can they be used to create geometric primitives?

Answer 4

In geometry, a half space is a region of space that includes all the points on one side of a flat, infinite plane. The term “half” is used because it divides space into two parts: one on the side of the plane, and the other on the opposite side. This flat, infinite plane is usually defined by an equation

Solid primitives are created by combining half spaces with Boolean operators

Question 5

Geometry assurance: Describe how a 3-2-1 locating scheme works

Answer 5

Six DOF are locked by six points
 Primary points A1, A2 and A3 defines a plane and locks the geometry in space in two
rotations and one translation: TZ, RX, RY
 Secondary points, B1 and B2, defines a line and locks the geometry in space in one rotation
and one translation: TY, RZ
 Tetriary point C1 locks the geometry in space in one translation: TX

Note:
1. Select a plane, choose 3 points in it that covers largest area
2. Select 2 other points that follows that line both in the “depth” of the solid
3. Select the last point to lock the figure in translating direction, the edge surface

Question 6

Computer graphics and virtual reality: Describe how the Z-buffer algorithm for depth sorting of objects drawn on a computer
screen works.

Answer 6

The Z-buffer algorithm sorts objects on a computer screen based on their depth. It works by assigning a depth value (Z) to each pixel. When rendering objects, it checks if the Z value of the current object is closer to the viewer than the Z value already stored for that pixel. If so, it updates the pixel’s color. This process ensures that closer objects appear in front of farther ones, creating a 3D effect in computer graphics.

When all polygons are checked the screen is updated with the color closest to the observe.

Question 7

Gouraud and Phong are two methods for rendering over multiple polygon surfaces. Describe
how they work.

Answer 7

Gourad:
 Calculate normal vector for all polygon surfaces
 Calculate ”mean normal vectors” for the vertices of the polygon
 Mean normal + Illumination model => calculation of intensities (colors) in the vertices
 Intensity values are interpolated line by line over the polygon

Phong:
 Calculate normal vector for all polygon surfaces
 Calculate ”mean normal vectors” for the vertices of the polygon
 Surface normals are interpolated line by line over the polygon
 Surface normal + Illumination model => calculation of intensities (colors) in each pixel

Question 8

Describe how Parallel and Perspective Projections are calculated. What is the visible
difference (on screen) between the two projections?

Answer 8

In perspective projection, objects appear smaller when they are farther away. It’s like when you see a road and the lines converge in the distance. We use similar triangles to figure this out.

In parallel projection, objects keep the same size no matter how far they are. We do this by setting the z-coordinate to zero, like when you’re looking at a map, and all the places have the same size.

So, in short, perspective makes far things look smaller, while parallel keeps things the same size no matter how far they are.

Question 9

Geometry models, created in a CAD-system, are used by a number of different functions
(departments etc.) within the product development process. Describe some problems related
to this.

Answer 9

Different functions use different software requiring different file formats: problem with file
conversion
 Problem with access to the right models

Question 10

Mention three benefits of using virtual product models in the product realization process

Answer 10

Minimizing the need for costly physical prototypes
 Finding problems as early as possible in the development process (easier and cheaper to fix)
 Faster development process with efficient tools (time to market)

Question 11

Mention two advantages of using off-line programming.

Answer 11

Avoid costly mistakes with real machines
 Faster and more efficient programming
 Possibility to make new programs without stopping the production

Question 12

What is a digital mockup (DMU) and for what is it used?

Answer 12

A special type of component based assembly model developed to be able handle large
assemblies (> 1000 parts) from different CAD-systems
 Can be used for e.g. packaging studies and assembly simulation but not for e.g. calculation
of mass etc. Tringulated surface

Question 13

Curves used in geometry modeling can be of different order. What are the advantages and
disadvantages of higher order curves? (2p

Answer 13

Advantage: increased precision
 Disadvantages: risk for corrupt curves, increased calculation time

Question 14

What characterizes a geometrically robust assembly concept?

Answer 14

A geometrically robust design is a design that allows manufacturing and assembly variation without
jeopardizing function or aesthetics.

Question 15

Describe four different aspects that has to be considered when designing for injection
molding.

Answer 15

For example:
 Assign proper draft angles, rule of thumb: 1 deg. per inch cavity depth
 Wall thickness should be uniform, e.g. coring out could be used to avoid thick walls
 Compensate for shrinkage
 Locate parting line, ejector pins and gate appropriately
 Avoid sharp corners and small corner radiuses, gives stress concentration and hinders a
streamlined flow for the molten plastics

Question 16

Describe how solid models are created with CSG (Constructive Solid Geometry). (2p)

Answer 16

Solid models are created by manipulating “primitives” with Boolean operators (union, sections,
subtraction)

Question 17

Bézier curves are defined by the following equation: p(u)=Sum (i=o, n antal) p_i, B_i,n(u)
Describe the different components of the formula and what they are used for.

Answer 17

Pi: control points, defines the curve
 Bin: weight functions, defines how the different control points affect the curve
 n: Order of the curve
 n+1: number of control points
 u independent variable 1

Question 18

In CSG the concept of half spaces is used. Describe/exemplify how they work and how they
are used to define geometry. (3p

Answer 18

Real, analytical functions f(x, y, z) defined in 3D which splits the space in two half spaces:
 one half space where f(x, y, z) < 0
 one half space where f(x, y, z) > 0
 Example: Cylindrical half space 0222  ryx
Solid primitives are created by combining half spaces with Boolean operators

Question 19

NURBS is the most commonly used type of curves in modern CAD systems. What
geometrical forms can be represented with NURBS but not with Bézier or B-splines?

Answer 19

Bézier and B-splines cannot represent conical and circular forms exactly

Question 20

Computer aided tolerance: Describe Variation analysis:

Answer 20

Variation analysis (with MC)
 Calculates a statistical prediction of the variation in critical measures
 Statistical method – random data
 Tolerances on parts (inputs) are randomly generated within defined distributions, tolerances
and Cp
 Distributions for critical measures (outputs) are generated from thousands of iterations
 All kinematical relations and sensitivities are captured in a 3D assembly model

Question 21

Computer aided tolerance: Describe Contribution analysis:

Answer 21

Calculates a ranked list of how all input tolerances contributes to the variation in the critical
measures
 All input parameters are varied (one at the time) within their tolerances on 3 levels
 Max output is registered
 Contribution is calculated in percent as output_2/output_1

Question 22

Computer aided tolerance: Describe Stability analysis:

Answer 22

Can be used to analyze the influence of each part locating scheme on
o Variation amplification, color-coding
o Position stability of parts
o Critical product dimensions (Measures)
 It is done by disturbing each locating point with a unit disturbance
 And summarizing their contribution with RSS
 Is often used to evaluate different positioning systems

Question 23

Computer graphics and VR: describe Desktop VR w pros and cons

Answer 23

Desktop (”Fishtank”) VR
 PC (+tracker) (+glove) (+stereo glasses)
 Advantages
o High display resolution (1600x1200)
o Cheap
o Simple to use

Cons:
- lack of realism
- Interactive ;(

Question 24

Computer graphics and VR: describe Helmet w pros and cons

Answer 24

Function
o Some sort of helmet or glasses with one display for each eye
 Advantages
o Wider FOV
o Stereo viewing
o High degree of immersion
o Relatively cheap
o Simple to install
 Disadvantages
o Helmet weight 1 - 4 kg
o Isolation from the world
o Only one user
o Relatively low screen resolution

Question 25

Computer graphics and VR: describe Powerwall w pros and cons

Answer 25

Function
o Two or more projectors working together
o Special software to coordinate the picture
 Advantages
o Wide FOV
o Natural size (cars)
o Stereo display (with shutter or polarized glasses)
o High resolution (3200x1024)
 Disadvantages
o Not so high degree of immersion
o Advanced computers
o Advanced technology to obtain invisible edges between projectors
o Expensive

Question 26

Light from a point light source can be reflected in two ways from a surface in a computer
model, diffuse and specular. Describe the difference between diffuse and specular reflection.
(2p

Answer 26

Diffuse:
Light hitting the surface is spread equally in all directions => Placement of the light source
influences but not the placement of the observer.
Specular:
The appearance of smooth, polished, surfaces is dependent of both the placement of the light source
and the position of the observer, i.e. the light is reflected mostly in one direction

Question 27

Gouraud and Phong are two different methods to obtain smooth shading of triangulated
surfaces. Why is Gouraud called vertex shading and Phong pixel shading?

Answer 27

Gouraud:
The color of a triangle is calculated at each vertex (corner) with the normal at that corner. The color
is then interpolated over the surface of the triangle.
Phong: The normal at the vertices (corners) are interpolated over the surface of the triangle and the
color is calculated for each pixel.

Question 28

Give two examples of usage of ergonomic simulation with computer manikins. (2p)

Answer 28

Evaluation of user interfaces
 Evaluation of concepts for manual assembly

Question 29

What are the tree types of modeling components in a multi-body system dynamic
simulation? (3p)

Answer 29

Rigid bodies
 Constraints (joints, motions)
 Forces (gravity, spring/dampers, friction etc.)

Question 30

Mention two different usages of geometry models within production (2p)

Answer 30

Ergonomic simulation
 Off-line programming of industrial robots
 Off-line programming of NC-machines
 Off-line programming of CMMs

Question 31

Mention three benefits of using virtual product models in the product realization process

Answer 31

Minimizing the need for costly physical prototypes
 Finding problems as early as possible in the development process (easier and cheaper to fix)
 Faster development process with efficient tools (time to market)

Question 32

Describe the concepts of Component based and Feature based assembly modeling (2p)

Answer 32

Component based assembly modeling:
 The position of the part in the assembly is determined by specifying its position and
orientation in global or relative coordinates
Feature based assembly modeling:
 Associates form features on different parts
 handles restrictions on form, position, orientation etc between mating form features
b)
 A feature
o is a physical part of a detail
o can be linked to a generic form
o has a specific engineering role (function, manufacturing method, simulation method, …)
o has predictable properties
c)
 Shorter lead-times and product lifecycles
 Increased complexity: variants, functions, components etc.
 Collaborative product development
d)
Applying guidelines for manufacturing already at the design stage leads to:
 Reduced manufacturing cost
 Shortened lad time

Question 33

What characterizes a feature (in the geometry modeling context)? (3p)

Answer 33

A feature
o is a physical part of a detail
o can be linked to a generic form
o has a specific engineering role (function, manufacturing method, simulation method, …)
o has predictable properties

Question 34

Mention three reasons for the increased industrial need for IT support for product
development (3p)

Answer 34

Shorter lead-times and product lifecycles
 Increased complexity: variants, functions, components etc.
 Collaborative product development

Question 35

Mention two reasons why it is important for the designer to have knowledge about the
manufacturing process.

Answer 35

Applying guidelines for manufacturing already at the design stage leads to:
 Reduced manufacturing cost
 Shortened lead time