Geometry modeling

Question 1

Why are conventional curves, such as y=f(x) or f(x,y)=0, not suitable for CAD?

Answer 1

Since they ar coordinate system depandant and hard to transform

Question 2

What type of curves should you use when CADing?

Answer 2

Parametric

Question 3

What are Bézier curves?

Answer 3

An approximate curve where a number of control points defines a characteristic polygon.
The order of the polynomial=number of control points -1

Question 4

What geometrical forms can’t be represented by Bézier curves och B-splines?

Answer 4

They can’t represent conical and circular forms exactly

Question 5

Explain the equation for the Bézier curve

Answer 5

Pi: control points, defines the curve
Bi,n: weight functions, defines how the different control points affect the curve
n: order of the curve
n+1: number of control points
u: independant variable 0<=u<=1

Question 6

What are B-spline curves?

Answer 6

• Further development of Bézier curves. As Bézier they are based on a polygon with a number of control points.
• Allows for better local control of the curve and the order of the polynomial doesn’t increase with the number of control points.
• Makes it easier to define joined curve segments.
• Each segments is controlled by the 4 closes control points.
• For B-splines the weight funtions are more local than for Bézier curves - affects a smaller part of the segment

Question 7

Explain the equation for the B-spline

Answer 7

n+1: the number of control points
k-1: the order
Nj,k: the weight functions
ti: control point variables

Question 8

What are NURBS?

Answer 8

• Non-Uniform Rational B-splines
• Bézier and traditional B-splines can’t represent conical and circular forms exactly - rational parametric curves can do this
• Requiers the use of homogenous coordinates
• NURBS is the most commonly used curve type in modern CAD-systems

Question 9

What are surface models?

Answer 9

• Used in order to be able to create complex, sculptured surface
• Easier to create smooth, complex forms
• ## Commonly used in visualization applications

Question 10

What are volume/solid models?

Answer 10

• Aims at clearly and information wise completely describe a physical object in a computer
• Solid models support higher levels of functionality and automation than surface models
• Solid models allows the designer to work with higher level objects rather than points, curves and surfaces

Question 11

What are the requirements on solid models?

Answer 11

• Modeling ability
• Validity
• Clearness and uniquness
• Modeling language
• Compactness
• Computability

Question 12

What types of solid models are there?

Answer 12

• Decomposition models
• Constructive models
• Boundary representations

Question 13

What are decomposition models?

Answer 13

• Can be made out of voxels or cell based models
• Voxels: a solid is composed of a number of cubes.
• Cell based models: a solid is build up by polygons

Question 14

What are some pros and cons with decomposition models?

Answer 14

Pros:
- Good computability
- Suitable for different types of calculations
Cons:
- Is an approximation model
- Requires a lot of memory for high precision

Question 15

What are constructive models?

Answer 15

Solid models are created by manipulating “primitives” with Boolean operators (union, sections, subtraction)
- Half spaces: solid models are created by combining half spaces with boolean operators
- CSG-models: solid models are created by combining sub-solids in form of parametric primitives (cyliner, sphere, cone…)

Question 16

What are some pros and cons with constructive models?

Answer 16

Pros:
- It is very compact (do not require a lot of memory)
Cons:
- It is hard to handle general surfaces

Question 17

What is boundary representation?

Answer 17

• The solid is defined with points, curves and surfaces plus a definition of what is inside the model
• Uses graphical methods such as sweep and rotate

Question 18

What are some pros and cons with boundary representation?

Answer 18

Pros:
- Can use parametric surfaces
- Can use boolean methods
Cons:
- Low compactness -> more memory is required

Question 19

Modeling systems based on CSG and boundary representation have important limitations in an engineering context, what are those?

Answer 19

• Requires exact specification of geometry and dimensions
• Tiresome modeling

Question 20

What is the definition of features?

Answer 20

• Is a physical part of a detail
• Can be linked to a generic form
• Ha a specific engineering role (ex. manufacturing or simulation method)
• Has predictable properties
  *A feature based product model describes a part or an assembly in terms of its features

Question 21

What types of features are there?

Answer 21

• Form features: commonly used shapes
• Tolerance features: deviation from nominal shape, position or orientation
• Assembly features: mating conditions, position and orientation
• Functional features: design intent, non-geometric attributes, performance etc.
• Material features: material composition, surface treatment etc.

Question 22

What do you need to consider regarding assembly development?

Answer 22

• Kinematics
• Interchangeability/variants of parts
  -Geometric layout for effective packaging
• Assembleability/deassembleability
• Collisions and interference
• Tolerance chains and tolerance allocation

Question 23

What does an assembly model need to include?

Answer 23

• Hierarchical relations: assembly -> sub-assemblu -> part
• Mating conditions: geometrical restrictions etc.
• Position and orientation of sub-assemblies and parts, globally and locally
• Mechanical degrees of freedom