BCA 4th Sem---Quadric Surface

• UNIT-I 

~The Advantages of Interactive Graphics
~Representative Uses of Computer Graphics 
~Classification of Application Development of Hardware and software for computer Graphics
~Overview, Scan:
~Converting Lines
~Scan Converting Circles
~Scan Converting Ellipses

UNIT-II 

~Hardcopy Technologies
~Display Technologies
~Raster-Scan Display System
~Video Controller
~Random-Scan Display processor
~Input Devices for Operator Interaction
~Image Scanners
~Working exposure on graphics tools like Dream Weaver, 3D Effects etc
~Clipping
~Southland- Cohen Algorithm
~Cyrus-Beck Algorithm
~Midpoint Subdivision Algorithm

UNIT-III 

~Geometrical Transformation
~2D Transformation
~Homogeneous Coordinates and Matrix Representation of 2DTransformations 
~composition of 2D Transformations
~The Window-to-Viewport
Transformations

~Introduction to 3D Transformations Matrix

UNIT-IV 

Representing Curves & Surfaces----

Polygon meshes parametric

Cubic Curves

Quadric Surface

Solid Modeling   Representing Solids

Regularized Boolean Set Operation primitive Instancing Sweep   Representation
Boundary Representations
Spatial Partitioning Representations
Constructive Solid Geometry Comparison of Representations

UNIT-V                           

~Multimedia Definition
~CD-ROM and the multimedia highway
~Computer Animation
(Design, types of animation, using different functions)

UNIT-VI  

~Uses of Multimedia
~Introduction to making multimedia –
~The stage of Project
~hardware & software requirements to make good multimedia skills
~Training opportunities in Multimedia Motivation for Multimedia usage

Quadric Surface

Quadratic surfaces

In this appendix we will study several families of so-called quadratic surfaces, namely surfaces z = f(x; y) which are de¯ned by equations of the type

Ax² + By²+ Cz² + Dxy + Exz + Fyz + Hx + Iy + Jz + K = 0; ------------(A.1)

with A;B;C;D;E; F;H; I; J and K being fixed real constants and x; y; z being variables. These surfaces are said to be quadratic because of all possible products of

two of the variables x; y; z appear in (A.1).

In fact, by suitable translations and rotations of the x; y and z coordinate axes it

is possible to simplify the equation (A.1) and hence classify all the possible surfaces

into the following ten types:

1. Spheres

2. Ellipsoids

3. Hyperboloids of one-sheet

4. Hyperboloids of two sheets

5. Cones

6. Elliptic paraboloids

7. Hyperbolic paraboloids

8. Parabolic cylinders

9. Elliptic cylinders

10. Hyperbolic cylinders

It is a requirement of this calculus course that you should be able to recognize, classify and sketch at least some of these surfaces (we will use some of them when doing triple integrals). The best way to do that is to look for identifying signs which tell you what kind of surface you are dealing with. Those signs are:

•  The intercepts: the points at which the surface intersects the x; y and z axes.
•  The traces: the intersections with the coordinate planes (xy-, yz- and xz-plane).
•  The sections: the intersections with general planes.
• The center: (some have it, some not).
•  If they are bounded or not.
•  If they are symmetric about any axes or planes.

Spheres

A sphere is a quadratic surface defined by the equation:

(X-X₀)²+(Y-Y₀)²+(Z-Z₀)²=R²------------------- (A.2)

the point (x0; y0; z0) in the 3D space is the center of the sphere. The points (x; y; z)

in the sphere are all points whose distance to the center is given by r. Therefore:

(a) The intercepts of the sphere with the x; y; z-axes are the points

(X₀ ± r; 0; 0), (0; Y₀±r; 0) and (0; 0; Z₀ ± r.)

(b) The traces of the sphere are circles or radius r.

(c) The sections of the sphere are circles of radius r0 < r.

(d) The sphere is bounded.

(e) Spheres are symmetric about all coordinate planes.

Next TopicSolid Modeling   Representing Solids

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