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Orthographic Projection, Drawing: A Comprehensive Guide.
In this article, You gonna learn about Orthographic Projection, Drawing; Its views, principles, systems i.e.,first angle projection, third angle projection.
Orthographic Projection, Drawing: A Comprehensive Guide.
December 1, 2018
In this article, You are going to learn about Orthographic Projection, Drawing; Its views, principles, drawing methods, systems, i.e., first angle projection, third angle projection.
So, Let’s Get Started.
Orthographic Projection.
Table of Contents [show]
This is such a type of drawing in which Parallel Projection is used for the preparation of the drawing of an object.
These lines are perpendicular to the plane.
In this drawing, it is assumed that the object is at infinity.
The shape of an object is seen in actual size in such drawing.
A plane is an imaginary surface on which pictures are prepared imaginably. Then it is transferred to the paper.
This plane is faced toward the object whose view is to be prepared.
Generally, three views of an object are prepared. These are Top View, Front View, and Side View.

If the plane is kept in a vertical position, then it is called the vertical plane.
If the plane is kept in a horizontal position, then it is called the horizontal plane.
The plane, horizontal or vertical, which are kept perpendicular to each other are called Principal Planes.
These include the Frontal Plane, Profile Plane, and Horizontal Plane: In addition to this, if a plane is placed at any other place, then it is called Auxiliary Plane.
These are used to draw inclined surfaces of an object. If these are placed in such a way that they form four Quadrants, then this figure is called Dihedral angle.
If these are placed in such a way that they form eight quadrants, then this figure is called Trihedral angle.
If the first Quadrant is used to draw the projections, then this system is called First Angle System.
If the third quadrant is used, then this system is called the Third Angle System.
In the First Angle System, the top view is placed below while the front view is upward and the side view is by the side of the front view.
In the Third Angle System, the top view is upward while the front view is downward and the side view is towards, aside from the front view.
Views of Orthographic Projection.
Following views are formed of an object in Orthographic Projection.
1. Front View.
2. Top View.
3. Back View.
4. Bottom View.
5. Right Side View.
6. Left Side View.

Generally, the Following Three views are prepared in the orthographic drawing.
1. Front View:
This view is prepared by placing the object in front. The length and height of an object are shown in this view.
2. Top View:
This view is prepared by looking to the object from the upper side. The length and breadth of the object are shown in it.
3. Side View:
This view is prepared by looking to the object from the right side or left side. The breadth and height of the object are shown in it.
Watch the video below for better understanding.
Principal Plane.
A plane is an imaginary and invisible clear surface. The drawing constructed on this imaginary curtain is transferred on the drawing sheet.
For example, if we look at some object through glass or plastic piece, then the picture of the object will be seen there.
This piece will work as a plane.
However, this plane is not a material body.
It is only an imaginary curtain, which is used to give the shape of a drawing by placing it in different positions.
This plane can be put in different positions.
However, the plane placed in the following positions is called the Principal Plane.
Besides such positions, the plane will be called Auxiliary Plane.
1. Frontal Plane.
2. Profile Plane.
3. Horizontal Plane.
1. Frontal Plane.
Such a plane which is placed in front of an object, while projections are drawn, is called the Frontal plane.
2. Profile Plane.
Such a plane which is placed to the right or left of an object. Side view of the object is drawn on this plane.
3. Horizontal Plane.
This is a plane which is placed upward or downward in the horizontal position of an object. Top view of the object is constructed on this plane.
Read Also: Perspective Projection, Drawing – Its Types, Objectives, Methods.
Drawing of Orthographic Projection.
For drawing Orthographic Projection, different planes are placed in a particular order.
Then a specific view is drawn through every plane.
A plane is placed in the following two Methods.
1. Dihedral Angle.
2. Trihedral Angle.
1. Dihedral Angle.
In this method, two principal planes are kept perpendicular to each other. One of these planes is Frontal, while other is horizontal.
Four right angles are obtained in this way which is called Dihedral Angle.
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स्रोत : brainly.in
Orthographic projection

Orthographic projection
From Wikipedia, the free encyclopedia
For the orthographic projection as a map projection, see Orthographic map projection. For mathematical discussion in terms of linear algebra, see Projection (linear algebra).
Part of a series on
Graphical projection
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Orthographic projection (also
orthogonal projection and
analemma)[a] is a means of representing three-dimensional objects in two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane,[2] resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are orthogonal to the projection plane.
The term sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the .[2] If the principal planes or axes of an object in an orthographic projection are parallel with the projection plane, the depiction is called or an . ( is synonymous with .) Sub-types of include , , and ; sub-types of include , , and .
A lens that provides an orthographic projection is an object-space telecentric lens.
Geometry[edit]

Comparison of several types of graphical projection
Various projections and how they are produced

The three views. The percentages show the amount of foreshortening.
A simple orthographic projection onto the plane = 0 can be defined by the following matrix:
{\displaystyle P={\begin{bmatrix}1&0&0\\0&1&0\\0&0&0\\\end{bmatrix}}}
For each point = (, , ), the transformed point would be
{\displaystyle Pv={\begin{bmatrix}1&0&0\\0&1&0\\0&0&0\\\end{bmatrix}}{\begin{bmatrix}v_{x}\\v_{y}\\v_{z}\end{bmatrix}}={\begin{bmatrix}v_{x}\\v_{y}\\0\end{bmatrix}}}
Often, it is more useful to use homogeneous coordinates. The transformation above can be represented for homogeneous coordinates as
{\displaystyle P={\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&0\\0&0&0&1\end{bmatrix}}}
For each homogeneous vector = (, , , 1), the transformed vector would be
{\displaystyle Pv={\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&0\\0&0&0&1\end{bmatrix}}{\begin{bmatrix}v_{x}\\v_{y}\\v_{z}\\1\end{bmatrix}}={\begin{bmatrix}v_{x}\\v_{y}\\0\\1\end{bmatrix}}}
In computer graphics, one of the most common matrices used for orthographic projection can be defined by a 6-tuple, (, , , , , ), which defines the clipping planes. These planes form a box with the minimum corner at (, , -) and the maximum corner at (, , -).[3]
The box is translated so that its center is at the origin, then it is scaled to the unit cube which is defined by having a minimum corner at (−1,−1,−1) and a maximum corner at (1,1,1).
The orthographic transform can be given by the following matrix:
{\displaystyle P={\begin{bmatrix}{\frac {2}{{\text{right}}-{\text{left}}}}&0&0&-{\frac {{\text{right}}+{\text{left}}}{{\text{right}}-{\text{left}}}}\\0&{\frac {2}{{\text{top}}-{\text{bottom}}}}&0&-{\frac {{\text{top}}+{\text{bottom}}}{{\text{top}}-{\text{bottom}}}}\\0&0&{\frac {-2}{{\text{far}}-{\text{near}}}}&-{\frac {{\text{far}}+{\text{near}}}{{\text{far}}-{\text{near}}}}\\0&0&0&1\end{bmatrix}}}

which can be given as a scaling followed by a translation of the form
{\displaystyle P=ST={\begin{bmatrix}{\frac {2}{{\text{right}}-{\text{left}}}}&0&0&0\\0&{\frac {2}{{\text{top}}-{\text{bottom}}}}&0&0\\0&0&{\frac {2}{{\text{far}}-{\text{near}}}}&0\\0&0&0&1\end{bmatrix}}{\begin{bmatrix}1&0&0&-{\frac {{\text{left}}+{\text{right}}}{2}}\\0&1&0&-{\frac {{\text{top}}+{\text{bottom}}}{2}}\\0&0&-1&-{\frac {{\text{far}}+{\text{near}}}{2}}\\0&0&0&1\end{bmatrix}}}

The inversion of the projection matrix , which can be used as the unprojection matrix is defined:
{\displaystyle P^{-1}={\begin{bmatrix}{\frac {{\text{right}}-{\text{left}}}{2}}&0&0&{\frac {{\text{left}}+{\text{right}}}{2}}\\0&{\frac {{\text{top}}-{\text{bottom}}}{2}}&0&{\frac {{\text{top}}+{\text{bottom}}}{2}}\\0&0&{\frac {{\text{far}}-{\text{near}}}{-2}}&-{\frac {{\text{far}}+{\text{near}}}{2}}\\0&0&0&1\end{bmatrix}}}

Types[edit]
Classification of orthographic projection and some 3D projections
Three sub-types of orthographic projection are , , and , depending on the exact angle at which the view deviates from the orthogonal.[2][4] Typically in axonometric drawing, as in other types of pictorials, one axis of space is shown to be vertical.
स्रोत : en.wikipedia.org