Computer Graphics in Mechanical engineering

Computer Graphics

1. Module-1

Computer Graphics

2. Computer graphics refers to the field of computer science that focuses on
creating, manipulating, and displaying visual images and animations using
computers.

Key Techniques in Computer Graphics:
●Rendering: The process of generating a visual image from a 3D scene.
Rendering can be real-time (e.g., in video games) or offline (e.g., in movies).
●Ray Tracing: A rendering technique that simulates the way light interacts
with objects to create photo-realistic images, often used in high-quality
animations and movies.
●Animation: The process of creating movement and transitions between
images to simulate motion.

3. CAD/CAM in product life cycle
•CAD is used for modeling, analysis, and documentation. It can help reduce design time and
complexity, and improve the quality of the design.
•CAM is used for planning, control, and support applications.
•CAD/CAM allows for digital simulation and testing of designs before manufacturing, which
can reduce the risk of costly mistakes and material waste.
• It helps manufacturers optimize product concept early in Design process, enabling them to
significantly improve product quality, while reducing product development time and cost.
•CAD/CAM integration can help streamline processes (from design to production) thus
increasing efficiency and productivity.
•It allows for easy modifications and adjustments throughout the product life cycle.

4. Product cycle (Design & Manufacturing)
Driver

5. Product cycle (Revised with CAD/CAM)

6. CAD/CAM hardware and software
•Hardware: Computers, visual displays/ graphic display terminals,
keyboards, mouse, light pen, dialogue systems, Graphical printers,
plotters, Storage devices
•Software: Programs to implement (calculation, archiving, and
presenting graphics) computer graphics on the system, Application
programs to facilitate engineering programs.
•Some examples of CAD/CAM software: Solid works, solid edge, ProE,
CATIA, openSCAD, Autodesk Fusion 360

7. There are two main categories of computer graphics:
1.2D Graphics: These are images created in two dimensions (width and height) and
include things like photos, illustrations, icons, and graphical user interfaces.
Common techniques for creating 2D graphics include raster graphics and vector
graphics.
○Raster Graphics: Images represented as a grid of pixels (e.g., PNG, JPEG, GIF).
○Vector Graphics: Images created with paths defined by mathematical equations
(e.g., SVG, EPS).
2.3D Graphics: These involve images and animations that represent three-dimensional
objects and scenes. In 3D graphics, depth is added to the width and height, and
objects are rendered to simulate perspective and lighting. This is used in applications
like 3D modeling, animations, video games, and virtual reality.
○3D Modeling: The process of creating a mathematical representation of a 3D
object.
○Rendering: The process of generating a 2D image or animation from a 3D model.
○Shading: The process of simulating how light interacts with surfaces to create
realistic effects.

8. 2D graphics 3D graphics
Represent objects on a flat surface, using only height
and width.
Represent objects in three dimensions, using height,
width, and depth which provides an element of
realism.
Often used in graphic design, traditional animation,
cartoons and illustrations.
Often used in video games and animation.
Common techniques for 2D designs include
rasterization and vector graphics.

3D graphics are created using polygons, textures, and
computer rendering to simulate real-world scenes.
Basic Elements: Points, Lines, Shapes, images, text Basic Elements: Vertices, Edges, Face, Textures
Rendering: Typically uses pixel-based or vector-based
rendering.
Pixel-based (Raster): Images are made of a grid of pixels
(e.g., BMP, JPEG, PNG).
Vector-based: Uses mathematical formulas to define
shapes (e.g., SVG, AI).
Rendering: Converts 3D models into 2D images with
perspective and lighting.
Wireframe: Represents the edges of a 3D model.
Shaded: Includes surface shading, textures, and lighting

Applications: UI/UX design, web graphics, 2D games,
digital art, and print media.
Applications: 3D modeling, animation, video games,
virtual reality, and simulations
Tools: Adobe photoshop, Adobe Illustrator, CorelDRAW3D Graphics: Blender, AutoCAD, SolidWorks

9. Applications in Engineering
•Design and Prototyping: Creating detailed designs and virtual
prototypes.
•Simulation: Visualizing and analyzing systems under different
conditions.
•Visualization: Enhancing understanding of complex systems through
visual representation.

10. Geometric Modeling
•Computer geometric modelling is the mathematical representation of
geometric elements to represent and manipulate graphical images on a
computer screen.
•A geometric model contains description of the modelled object's shape.

Geometric modeling systems can be categorized into three types based
on how they represent objects.

1.Solid modeling:
Also known as volume modeling, this is the most widely used method. It
provides a complete description of a solid object by defining its nodes,
edges, and surfaces. All the information required for manufacturing can
be obtained with this technique.

11. Geometric Modeling
2. Surface modeling:
This method captures the complex surfaces that define a product's
visual and tactile characteristics. Surface models are more complicated
than wireframe models but not as refined as solid models.

3. Wireframe modeling:
It involves creating a visual representation of a 3D object using lines and
vertices to define its edges and surfaces, without solid faces or textures.

13. Mapping of Geometric Models
•Mapping of geometric models in CAD involves changing the
description of a set of points or a point from one coordinate system
to another.

•The position and orientation of the model remain the same in space,
but the descriptions of these positions and orientations change.

•Rotational mapping where both systems share the same origin but
have a different orientation by an angle θ.

•Translational mapping where the axes are parallel. Origins of both
systems are different but their orientations in space are same.

14. Parametric representation
of curves and surfaces

15. Parametric representation
•Parametric representation is a powerful mathematical approach for defining
curves and surfaces in computer graphics and engineering.
•It allows for flexible, precise modeling of geometric shapes by expressing the
coordinates as functions of one or more parameters.
•In parametric form, the curve is represented as



where X, Y, Z are the coordinate values on the space curve, and the
corresponding functions x, y, z are the polynomials in a parameter, u.
This representation permits to quickly compute the individual X, Y, Z
coordinates of all the points on the curve.

16. Advantages of Parametric Representation
•Flexibility: Easily describe complex shapes and motion paths.
•Continuity: Smooth and continuous descriptions of curves.
•Control: Direct control over the shape using parameters.
•Precision: High level of detail and control over shape and motion.
•Smoothness: Natural handling of curves and surfaces with continuous
derivatives.
•Compact Representation: Efficient storage and manipulation of
geometric data.

17. Applications in Engineering and Graphics
•CAD Systems: Design and modeling of complex mechanical components
and architectures.
•Animation: Defining paths and surfaces for characters and objects.
•Simulation: Accurate representation of physical phenomena (e.g., airflow
over surfaces).
•Visualization: Creation of detailed and realistic renderings of objects.

Challenges
•Complexity: Managing multiple parameters and ensuring smooth
transitions.
•Computation: Requires significant computational resources for rendering
and manipulation.
•Design: Needs careful control point placement and parameter tuning to
achieve desired shapes.

18. Free form surfaces
•There may be surfaces which cannot be defined by any of the analytical
techniques available. A few examples are car bodies, ship hulls, some
die-cavity surfaces, decorative surfaces styled for aesthetics.

•The only way these surfaces can be modelled is through a series of control
points and other boundary conditions, which specify the nature of the
surface desired.

•Some of the techniques that are normally employed in CAD systems are
Bézier surfaces, B-spline surfaces, and NURBS.

19. Synthetic Curves
•Synthetic curves are curves generated through mathematical algorithms
or computational methods.
•Used to create complex shapes and paths.
•Unlike analytic curves (such as circles or ellipses, which have explicit
equations), synthetic curves are often defined by a set of control points
and basis functions, allowing for greater flexibility in shape design.
•There are a number of mathematical techniques available for handling
non-analytical surfaces such as Bézier and B-splines

20. Bézier Curves
•Parametric curves defined by a set of control points where the curve is
calculated as a weighted sum of these points.
•The curve is a linear combination of these control points and basis polynomials
(Bernstein polynomials).
•It uses the vertices as control points for approximating the generated curve.
The curve is pulled towards its control points but does not necessarily pass
through them (except the first and last points).
•It is contained within the convex hull of its control points.
•The flexibility of the process can be seen by changing the position of the individual control
points in space, thereby altering the control polygon.

21. Bézier Curves
•Changing the second point in space, alters the curve as shown. This is a very flexible process
and is widely used for the design of aesthetic surfaces.
•The flexibility of the curve increases with more control points. The process can be extended
for surfaces as well.
•The degree of the polynomial defining the curve is one less tham the number of control
points.

22. Numerical Formulation

23. Bézier Curves
Applications:

1.In CAD/ CAM for designing curves for engineering and manufacturing
2.In vector based graphic design (e.g Adobe Illustrator)
3.In Animation for smooth transitions and paths for object movement.
4.In Typography for defining character outlines in scalable vector fonts.

24. B-Spline Curves
•In the case of Bézier curves, it is considered as a single curve controlled by
all the control points. As a result, with an increase in the number of
control points, the order of the polynomial representing the curve
increases.
•An alternative is to use a B-spline (Basis Splines) to generate a single
piecewise parametric polynomial curve through any number of control
points with the degree of the polynomial selected by the designer.

•They provide greater flexibility and control over curve shaping by dividing
the curve into segments influenced by a smaller subset of control points,
offering local control and the ability to represent more complex shapes
efficiently.
•Defined by control points and a set of basis functions.

27. B-Spline Curves
Characteristics:
•Local control: Moving a control point affects only a portion of the curve.
•Smoothness: B-spline curves are continuously differentiable up to k−1
times.

Applications:
•In CAD for Creating precise, smooth curves and surfaces
•In Animation for designing motion paths and character animations.
•In Image Processing for Smoothing and curve fitting in image analysis.
•In Engineering for representing curves for simulations and manufacturing.

28. B-Spline Curves
NURBS (Non-Uniform Rational B-Splines)
•Definition: A more versatile form of B-spline that includes weights for each control
point, allowing for the representation of both standard geometric shapes (e.g., circles)
and free-form shapes.
•Characteristics:
•Can exactly represent conic sections (circles, ellipses, parabolas).
•Flexible for complex and precise modeling.
•Applications: Used in automotive and aerospace industries, CAD, and 3D modeling
software for designing complex surfaces.

29. Hermite Curves
•It is an interpolating piecewise cubic polynomial and is specified based on
position and gradient at each end point of curve i.e. two endpoints and two
tangent vectors.
•Useful for creating smooth transitions between points while maintaining
control over the shape of the curve.
•The curve is typically parameterized by a single variable t, where t ranges from
0 to 1 as you move along the curve.
•The curve can be adjusted locally as each section is dependent on its endpoint
constraints.
•The tangents determine the curve's slope at the endpoints. By adjusting the
values of the tangents, you can change the shape of the curve without
altering the endpoints.

30. Hermite Curves

31. Hermite Curves
Applications:
•widely used in graphics and animation for creating smooth transitions
between keyframes.
•In computer-aided design (CAD), Hermite curves are often used to
design smooth paths or shapes.
•In robotics or game development, Hermite curves can help interpolate
smooth paths for objects or characters.

32. Surface Representation
Surface representation in CAD (Computer-Aided Design) and CAM (Computer-Aided
Manufacturing) is a critical aspect of 3D modeling and design, enabling the creation,
visualization, and manipulation of complex shapes and surfaces used in manufacturing
and engineering applications. Surfaces define the outer boundaries or skin of 3D
objects and are essential in a wide range of industries, including automotive,
aerospace, and product design.

33. Parametric Surfaces: These are surfaces defined by mathematical equations or
parametric functions that depend on one or more parameters. Parametric surfaces are
useful for accurately describing complex shapes and allow for easy manipulation of the
surface.
Examples of Parametric Surfaces:
●Bezier Surfaces: Defined using control points, tangents, and weights. These
surfaces are useful for defining smooth curves and surfaces in 3D modeling and
design.
●B-Spline Surfaces: A more general form of parametric surfaces where the curve or
surface is influenced by a set of control points, and the surface is smooth and
continuous.
●NURBS (Non-Uniform Rational B-Splines): An extension of B-splines that
incorporates rational functions and allows for more flexible and complex surface
shapes. NURBS are widely used in CAD for their ability to represent both analytic
and free-form shapes.

34. Bezier Surfaces
A Bezier surface is defined by a grid of control points, similar to how Bezier
curves work, but extended to two parameters.
The surface is typically expressed as a linear combination of Bernstein
polynomials:




Bezier surfaces are widely used for smooth, curved surfaces in both CAD
and CAM applications. They are easier to control for design modifications,
making them highly practical in industrial design.

35. NURBS (Non-Uniform Rational B-Splines)
A NURBS surface is a rational B-spline surface defined by control points,
weights, and knot vectors, which allows for more accurate representation
of both simple geometric shapes (e.g., circles) and free-form surfaces.
The NURBS surface can be expressed as a weighted sum of B-spline basis
functions, allowing the designer to adjust the shape with a higher degree of
control.
Key Advantages of NURBS:
●Can represent both simple and complex shapes.
●Flexible control over the surface shape via control points and weights.
●Easily adjusted for design changes.

36. Applications of Surface Representation in CAD/CAM
Industrial Design and Engineering: Surface modeling allows engineers and designers to
create products with intricate and aesthetically pleasing shapes, such as car bodies,
airplane wings, and consumer electronics.
Aerospace and Automotive: In these industries, surfaces must be precise and
aerodynamic, and surface representations like NURBS and Bezier are commonly used
to design parts with complex curves and smooth transitions.
Product Design: For products with free-form shapes, like furniture, jewelry, or
consumer electronics, advanced surface representation is essential to creating
ergonomic and functional designs.
Animation and 3D Modeling: In visual effects and gaming, surfaces are used to create
realistic models of characters, objects, and environments.
Manufacturing: CAM uses surface representations to generate tool paths for CNC
machines, ensuring that complex geometries can be manufactured with high precision.
The tool paths depend on the surface definitions provided by CAD.