Construction of an isometric projection - transformation, Computer Graphics

Construction of an Isometric Projection - Transformation

In this projection, the direction of projection i.e. d = (d1,d2,d3) makes an identical angles with all the 3-principal axes. Suppose here that the direction of projection d = (d1,d2,d3) make equal angles as α with the positive side of the x,y, and z axes as in the Figure 13.

771_Sub Classes of Orthographic Projection.png

Subsequently

i.d=d1=|i|.|d|.cosα  => cosα=d1/|d|

Correspondingly

d2=j.d=|j|.|d|.cosα  => cosα=d2/|d|

d3=k.d=|k|.|d|.cosα  => cosα=d3/|d|

Consequently cosα=d1/|d| = d2/|d| = d3/|d|

ð    d1= d2 = d3   is actual

We select d1=d2=d3=1

So here, we have d =(1, 1, 1)

Because, the projection, we are seeing for is an isometric projection => orthographic projection, that is, the plane of projection, must be perpendicular to d, hence d = n = (1,1,1). We suppose here that the plane of projection is passing via the origin.

ð  We identify the equation of a plane which is passing via reference point R(x0,y0,z0) and consisting a normal

N = (n1,n2,n3) is: (x - x0).n1 + (y - y0).n2 + (z -z0).n3=0

Because (n1,n2,n3)=(1,1,1) and (x0,y0,z0)=(0,0,0)

From equation (14), we have x + y + z = 0

Hence, we have the equation of the plane: x + y + z = 0 and d = (1,1,1)

Posted Date: 4/4/2013 2:37:23 AM | Location : United States







Related Discussions:- Construction of an isometric projection - transformation, Assignment Help, Ask Question on Construction of an isometric projection - transformation, Get Answer, Expert's Help, Construction of an isometric projection - transformation Discussions

Write discussion on Construction of an isometric projection - transformation
Your posts are moderated
Related Questions
Algorithms for Basic Line Segment Plotting There are two important algorithms for basic line segment plotting-DDA algorithm and Bresenham algorithm.  Both the algorithms use th

Q. What is Monitor? A Monitor is a television like box connected to your computer and providing you a vision into the mind of your PC. It displays what your computer is thinki

refreh buffer

Advantages of GIF Files GIF is the most extensively supported graphics format upon the Web. GIFs of diagrammatic images appear better than JPEGs. GIF maintains inte

Three Dimensional Transformations A 3D geometric transformation is used extensively in object modelling and rendering.2D transformations are naturally extended to 3D situations

Picture Information - Raster Graphics and  Clipping Now, the picture information is accumulated in the form of bit plans on which all bit plane complete information of pictur

Question 1 Explain Bresenham's Circle Drawing Algorithm Question 2 Derive the matrix for inverse transformation Question 3 Discuss the following Raster Graphic Algorithm

QUESTION 1: a) Draw a Bezier curve showing the following components i. hull ii. curve CV iii. span iv. start and end point b) Maya provides highly effective tools for all t


Simulation: There are several things, places and events people cannot witness in first person. There are a lot of causes for this. Several may happen too rapidly, several may be t