Geometry modeling Flashcards
Describe the steps necessary to create a solid, using surface modeling, in a modern CAD system.
Wireframe element (Points, lines, planes, curves)
(Oversized) surfaces from these wireframes (sweep, resolve)
Trim the surfaces
Join surfaces to one element
Transform to sold (thick, closed surface)
(Add fillets)
Bézier curves are defined by the following equation: p(u)=sum_i=0_n(p_iB_i,n(u))
Describe the different components of the formula and what they are used for.
p = control points, used to define the curve
B = Weight function for the control point (how large influence they have)
n = order of the curve
n+1 = total number of control points
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?
NURBS can be used to represent circular and conical forms, but Bézier and B-splines cannot.
Mention three different aspects that have to be included in an assembly model (in e.g. a CAD system).
An assembly model needs to include:
Hierarchical relations
assembly -> sub-assembly -> parts
Mating conditions
geometrical restrictions, etc, constraints?
Mechanical degrees of freedom
How components can move or rotate relative to others, essential for assembly motion
Mention two advantages of using solid models instead of e.g. surface models.
You can measure their mass and moment of inertia
Solid models allows the designer to work with higher level of objects rather than points, curves and surfaces
Describe how solid models are created with CSG (Constructive Solid Geometry)
The use of boolean operators (union, sections, subtraction) of primitives shapes -> new shape
In CSG the concept of half spaces is used. Describe/exemplify how they work and how they are used to define geometry.
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 x^2 + y^2 - z^2 <0
Solid primitives are created by combining half spaces with Boolean operators.
H1, infinitely long
Cut it with infinite planes
The intersection of them is the cylinder
Describe the following three types of solid models, mention some advantages or disadvantages for each. Decomposition models, constructive models, boundary representation
Decomposition models: Solid build by voxels (cubes) or cell based models (polygons (often triangles)). Approximate model, lot of memory for high precision. Good computability.
Constructive models: Boolean operators, and use of primitives, half-spaces, CSG-models (constructive solid geometry). High compactness, some computer operations are computer intense.
Boundary representation: Points, lines/curves, surfaces + definition of what is inside the model. Can be invalid. Good computability, low compactness.
What do C^0, C^1, and C^2 continuity between two curve segments mean?
C^0: Same point, joined without constraints
C^1: Same point and direction at the common point
C^2: Same point, curvature at the common point
Curves used in geometry modelling can be of different order. What are the advantages and disadvantages of higher
order curves?
Advantages: increased precision
Disadvantages: risk of corrupt curves, increased calculation time
What order is usually used in CAD-systems?
3: rd.
Bézier and B-spline are two types of curves used in geometry modelling. What is the advantage of B-spline curves?
Better control of the curve
Order of the polynomial does not increase with the number of control points
Easier to define joined curve segment
Describe how trimmed parametric surfaces are defined/created.
Parametric surfaces are defined in similar way as parametric curves but with two parameters u and v.
Parametric curves are defined in the same 2D space
They are used to create holes (inner trim curve)
Or the outer boundary of the surface (outer trim curve)
The trimmed parametric surface is transformed to 3D space
What characterizes a feature (in the geometry modelling context)?
A feature
Is a physical part of a detail
Can be linked to a generic form
Has a specific engineering role
Has predictable properties
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
Different functions uses different software requiring different file-formats: problem with file conversion
Problem with access to the right model
