Plane equation - curves and surfaces, Computer Graphics

Plane Equation - Curves and Surfaces

Plane is a polygonal surface that bisects its environment in two halves. One is termed to as forward and another as backward half of some plane. Currently the question is that half is forward and that backward, since both are relative terms. Thus to get rid of this dilemma, we utilize the mathematical representation of planes, that is, concepts as equations of planes, normal to a plane and so on, that we have already studied. Now we know that both forward and backward halves are associative terms but with respect to what? Yes, it's the plane itself in respect of that we can say any point in the surrounding environment is in back or front of the plane. Hence we see any point on the plane must satisfy the equation of a plane to be zero, that is: Ax + By + Cz + D=0. This equation implies any point (x,y,z) will only lie upon the plane whether it satisfies the equation to be zero any point (x,y,z) will lie upon the front of the plane whether it satisfies the equation to be greater than zero and one of point (x,y,z) will lie upon the back of the plane whether it satisfies the equation to be less than zero.

Here (x, y, z) is any point on the plane, and the coefficients A, B, C and D are constants explaining the spatial properties of the plane? This idea of space partitioning is used commonly in method of BSP that is Binary Space Partitioning, trees generation a polygon representation scheme, fairly similar to Octrees.

The significance of plane equations is that they assist in producing display of any 3-D object, but for such we have to to process the input data representation for the object by several procedures that may include the follow steps of processing.

  • To transform the modeling and world-coordinate explanations to viewing coordinates,
  • To devise coordinates,
  • To know visible surfaces,
  • To apply surface-rendering processes
Posted Date: 4/4/2013 4:05:28 AM | Location : United States







Related Discussions:- Plane equation - curves and surfaces, Assignment Help, Ask Question on Plane equation - curves and surfaces, Get Answer, Expert's Help, Plane equation - curves and surfaces Discussions

Write discussion on Plane equation - curves and surfaces
Your posts are moderated
Related Questions
Cohen Sutherland algorithm Point clipping is very simple.  All you need to check is whether a point is inside the window extremes in x- and y-directions.  For line clipping sev

Linking: A hypermedia system and also information in general contains different types of relationships among various information parts. Illustrations of typical relationships comp

What are the advantages of electrostatic plotters?  They are faster than pen plotters and very high quality printers. Recent electrostatic plotters contain a scan-conv

Ellipse generating algorithm: Algorithm is similar to circle algorithm. We divide the ellipse on the positive quadrant into two regions. Region 1 where the slope > -1, and Reg

DV Encoder Type 1 : The video and audio streams are together interfaces by standard DV bit stream. Such format is fully supported through DirectShow which accepts this interleaved

OBJECTIVE Since graphics plays a very important role in modern computer application, it is important to know more information about its hardware and software operations. Despite

Image Processing Process Images are the last product of most processes in computer graphics. The ISO that is International Standards Organization explains computer graphics as


How we create virtual reality images for use on a computer system When a virtual tour of, for instance, a house is shown on a website the images need to be first created and th

Relation between polar coordinate system and Cartesian system A frequently utilized non-cartesian system is Polar coordinate system. The subsequent figure A demonstrates a pol