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
what languge do computers speak

2D Line Segment Generation  A digitally plotted line is basically an approximation of infinite number of points on an abstract line segment by only a finite number of points on

Use of Interactive Multimedia in Education Virtual reality, where 3-D experimental training can simulate real situations. Computer simulations of things too expensive,

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

To reflect the ball off of the polyline, we need to re?ect it off of the segment that had the minimum thit. But the reflection computation depends only on t hit , n, P and v, so th

CRT - Cathode Ray Tube Electron gun is used to send an electron beam aimed at a particular point on the screen. Deflection system is used to make the beam strike the screen



Event Driven Devices - Polling Polling: The status of all devices is periodically checked in a repetitive manner through a polling loop. While an event happens, the loop is

Anti- aliasing: Most aliasing artifacts, when appear in a static image at a moderate resolution, are often tolerable, and in many cases, negligible. However, they can have a signi