# What Is Translation Matrix?

Author: Loyd
Published: 4 Jan 2022

### Passive translation

A translation is a geometric transformation that moves a space by the same distance in a given direction. A translation can be seen as the addition of a constant vector to every point or the change of the origin of the coordinate system. Any translation is an isometry.

A horizontal translation is a transformation that results in a graph that is equivalent to shifting the base graph left or right. A graph is translated by moving points on it. lattice groups are finitely generated and are part of the three-dimensional translation group.

The entire group is generated by a finite set. While geometric translation is often seen as an active process that changes the position of a geometric object, a similar result can be achieved by a passive transformation that moves the coordinate system but leaves the object fixed. A translation of axes is known as a passive version of an active geometric translation.

### Shape Orientation: Translation of an Unknown Number

A type of transformation that occurs when a figure is moved from one location to another on the coordinate plane without changing its size, shape orientation is a translation. The coordinates of the translated figure can be found using matrix addition.

### The Camera Space Projector

The projection matrix determines the camera space, which is the visible area in a scene, so that the renderer knows to check for objects only in places that will be seen. It helps determine the clipping area by figuring out if objects are off screen and need to be retriangulated. You are moving away from thinking about the origin of the model to thinking about the origin of the world space.

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### Linear translations

The points in the object are moved in a straight line. The size, shape and orientation of the image are the same as the original object. The object and image are facing the same direction. A translation can be represented by a column matrix or column vector where a number of units to move right or left along the x- axis and a number of units to move up or down along the y- axis are all shown.

### The camera ToClipMatrix is GLSLsmat4

The matrix cameraToClipMatrix has the same properties as a GLSL mat4. The zero-based column of the matrix is returned as a vec4 if the mat4 is included in the array. A diagonal matrix is a type of matrix that is constructed using only a single value.

There is a matrix with zeros except for the diagonal from the upper- left to the lower-right. The value will be passed to the constructor. A diagonal matrix with 1 as the value is called an identity matrix.

### The image of a gravitational field in the counter-clockwise direction

The image gets shifted in the counter-clockwise direction if the angle is positive. The angle needs to be negative if you want to do a clockwise rotation.

### Positive values for scaling factors

Positive values are valid for scaling factors. Values less than 1 affect the size of objects and values greater than 1 increase the size of objects. The size of object does not change for Sx and Sy.

### Orthogonality of a matrix with less than or equal transpose

If the matrix has a transpose of less than or equal to the one found in the other matrix, it is a orthogonal matrix. Then, add the matrix to the transpose. If the product is an identity matrix, the given matrix is not.

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