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
GIF File Compression The Graphic Interchange Format file format utilizes a relatively basic form of file compression which squeezes out inefficiencies within the data storage w

What is scan line algorithm?  One way to fill the polygon is to apply the inside test. I.e. to check whether the pixel is inside the polygon or outside the polygon and then hig

Graphic Primitives In previous section, we have discussed refreshing display devices and its categories which are Raster and Random Scan display devices. We have also discusse

Traditional Animation techniques as: 1) Key Frames                        2) Cel Animation Formula: Required Key frames for a film = {[Time(in seconds)]

Reflection and Shear There are a few important transformations which are not primitive in the sense that they can be expressed as compositions of translation, rotation and scal

Sound and Audio: Sound is a mechanical energy disturbance which propagates by matter as a wave. Sound is characterized through the various properties that are: frequency, per

Algorithms for Identification of Observable Objects There are various algorithms for identification of observable objects for various types of applications. Several methods ne

Scan Line Algorithm A scan line algorithm determines the overlap intervals of the polygon with each scan line to obtain interior points of the polygon for assigning those point

If the spacing between the knot sequence is uniformly doubled, will the shape of the resulting B-spline curve change?  Justify your answer.

refreh buffer