3 Dimensional Angle Projection Research Paper

Three dimensional object projection on a two dimensional plane

Table of Contents

Introduction 3

Types of projection 3

Orthographic projection 3

Oblique projection 4

Introduction

Math is an important part in all sciences, especially computer science. That and the fact that I want to base my career in the field of computer science are the main reason I chose the topic “Three dimensional object projecting on a two dimensional plane”. The way of projecting a three dimensional object on a two dimensional plane has not changed that much over time. Projections are formed on the view plane that is in fixed relative to the position of the center of projection. Rays (projectors) projected from the center of projection

Axonometric projection divides in to three types: isometric, dimetric and trimetric projection.

In isometric projection (most commonly used in engineering drawing) the direction of viewing is such that the three axes of space appear equally foreshortened, and there is a common angle of 60 degrees between them. As the distortion caused by foreshortening is uniform the proportionality of all sides and lengths is preserved, and the axes share a common scale.

In dimetric projection, the direction of viewing is such that two of the three axes of space appear equally foreshortened, of which the attendant scale and angles of presentation are determined according to the angle of viewing; the scale of the third direction (vertical) is determined

(2010) in [http://mathworld.wolfram.com/PohlkesTheorem.html]. The constants a and b uniquely specify a parallel projection. When a and b are both zero, the projection is said to be "orthographic" or "orthogonal". Otherwise, it is "oblique". The constants a and b are not necessarily less than 1, and as a consequence lengths measured on an oblique projection may be either larger or shorter than they were in space. In a general oblique projection, spheres of the space are projected as ellipses on the drawing plane, and not as circles as one would expect them from an orthogonal projection.

Oblique is not really a 3D system but a two-dimensional view of an object with 'forced depth'. One way to draw using an oblique view is to draw the side of the object you are looking at in two dimensions, i.e. flat, and then draw the other sides at an angle of 45 degrees, but instead of drawing the sides full size they are only drawn with half the depth creating 'forced depth' – adding an element of realism to the object. Even with this 'forced depth', oblique drawings look very unconvincing to the eye. For this reason oblique is rarely used by professional designers and