Rotation about z-axis - transformation for 3-d rotation, Computer Graphics

Rotation about z-axis - Transformation for 3-d rotation

Rotation about z-axis is explained by the xy-plane. Suppose a 3-D point P(x,y,z) be rotated to P'(x',y',z') along with angle of rotation q see Figure 9. Because both P and P' lies upon xy-plane so z=0 plane their z components keeps similar as z=z'=0.

2469_Rotation about z-axis - Transformation for 3-d rotation.png

Figure a                                                                            Figure b

Thus, P'(x'y',0) be the effect of rotation of point P(x,y,0) making a +ive or anticlockwise angle φ with value of z=0 plane, as demonstration in Figure 10. From figure (10),

P(x,y,0) = P(r.cos φ,r.sin θ,0)

P'(x',y',0)=P[r.cos(φ + θ),rsin(φ + θ),0]

The coordinates of P' are as:

x'=r.cos(θ + φ) = r(cos θ cos φ - sin θ sin φ)

=x.cos θ - y.sin θ      (where x=rcos φ and y=rsin φ)

As the same;

y'= rsin(θ + φ)=r(sin θ cos φ + cos θ.sin φ)

=xsin θ +ycos θ

Hence,

1229_Rotation about z-axis - Transformation for 3-d rotation 1.png

Posted Date: 4/3/2013 6:06:35 AM | Location : United States







Related Discussions:- Rotation about z-axis - transformation for 3-d rotation, Assignment Help, Ask Question on Rotation about z-axis - transformation for 3-d rotation, Get Answer, Expert's Help, Rotation about z-axis - transformation for 3-d rotation Discussions

Write discussion on Rotation about z-axis - transformation for 3-d rotation
Your posts are moderated
Related Questions
In contrast to depth-buffer method, here we identify one surface at one time, scan-line method deals along with multiple surfaces. Since it processes each scan-line at one time, al

Softwares and Hardwares for Computer Animation The categories of both software as well as hardware needed to work on animation are now to be discussed. Computer animation can b

How avar values generate to get realistic movement There are numerous ways of generating avar values to get realistic movement. One way is to use markers on a real person (or w

What is scaling?  The scaling transformations changes the shape of an object and can be carried out by multiplying every vertex (x,y) by scaling factor Sx, Sy where Sx is the

Reflection and Types of Reflection Reflection and its types:   Reflection: this is the phenomenon of bouncing back of light; such phenomenon obeys laws of Reflec

mcqs of illustration in nts test

What is a spline?  To produce a smooth curve by a designed set of points, a flexible strip called spline is used. Like spline curve can be mathematically explained with a piece

Question 1 Discuss the general properties of analog signal Question 2 Differentiate images and graphics Question 3 Explain the video compression standard H.263

Two-Dimensional Geometric Transformations  When a real life object is modelled using shape primitives, there are several possible applications.  You may be required to do furth

File Formats that are used for Bitmap Data Bitmap data can be saved in a wide variety of file formats are: • BMP: restricted file format that is not appropriate for use in