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Grammar and spelling
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lordlatch committed Mar 15, 2017
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26 changes: 13 additions & 13 deletions docs/user_guide/nodes/matrix/change_matrix_pivot.rst
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Expand Up @@ -3,21 +3,21 @@ Change Matrix Pivot

Description
-----------
This node includes 5 operations which are combined transformation that enable
you to change the pivot of theinput transformation matrix.
This node includes 5 operations which are combined transformations that allow
you to change the pivot of the input transformation matrix.

.. image:: images/change_matrix_pivot_node.png
:width: 160pt

Demonstration
-------------

Technically there is no thing called a **Pivot** in mathematics. There is a constant
Technically there is no such thing as a **Pivot** in mathematics. There is a constant
pivot which is the **Origin** (point ``(0,0,0)``) of the coordinates space.
However we can perform a fake transformation to change the pivot of the original transformation.

**Example**: Suppose we have a cube at position ``(2,2,0)``, if you multiplied
the matrix of the cube by a **Z axis rotation transformation matrix** the cube
the matrix of the cube by a **Z axis rotation transformation matrix**, the cube
will rotate around the origin point which is ``(0,0,0)`` and its location will
linearly change relative to that origin.

Expand All @@ -35,15 +35,15 @@ it was which is defined mathematically as **adding**.
.. image:: gifs/change_matrix_pivot_node_example_2.gif

In Animation nodes the pivot is a bit different. Since the location of the object
is stored in the *Homogeneous Coordinates Transformation Matrix*, its pivot exist
is stored in the *Homogeneous Coordinates Transformation Matrix*, its pivot exists
in the objects local space coordinates.

Options
-------

- **Pivot Matrix**
This option allow you to change the pivot using a transformation matrix. This
will enable you to set a parent child relation between the matrix and the pivot
This option allows you to change the pivot using a transformation matrix. This
will aloow you to set a parent child relation between the matrix and the pivot
matrix. The location of the pivot matrix does not affect the pivot but the
rotation and the scale does relative to the point ``(0,0,0)``.

Expand All @@ -52,27 +52,27 @@ Options
- **Pivot Location**
This option will let you choose the location of the pivot in 3D space.
Notice that the original pivot location is in the local space so if you want
to better unserstand how this node work, match the pivot of the world space
to better unserstand how this node works, match the pivot of the world space
coordinates and the local space coordinates by placing the object at the point ``(0,0,0)``.

.. image:: gifs/change_matrix_pivot_node_example_4.gif

- **Center And Rotation**
This option enable you to change the pivot in the local space coordinates as
This option allows you to change the pivot in the local space coordinates as
well as a built in rotation around the pivot of the world space coordinates.
Notice that that pivot of the local space coordinates is relative to the
difference in the world space coordinates.

.. image:: gifs/change_matrix_pivot_node_example_5.gif

- **X Line,Z Direction**
This option allow you to set the location of the pivot and orient the
This option allows you to set the location of the pivot and orient the
local space of the transformation matrix to a specific orientation based
on 2 vectors. A point that make a vector with the origin which define the
x axis of the local space and a normal vector whic correspond to the local
z axis of the local space. The default value for the normal vector is the
``(0,0,1)`` which align the the local Z axis with the global Z axis which
is the standard orientatioin, however if you change the the normal to be
``(0,0,1)`` which aligns the the local Z axis with the global Z axis which
is the standard orientation, however if you change the the normal to be
``(1,0,0)`` this means you are aligning the local Z axis with the global
X axis which means a rotation around the Z axis actually correspond to a
rotation around the X axis.
Expand All @@ -81,7 +81,7 @@ Options

- **X Line, Z line**
This is exactly like **X Line,Z Direction** explained above, but instead of
the normal vector you have a line that define the Z orientation.
the normal vector you have a line that defines the Z orientation.

Inputs
------
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2 changes: 1 addition & 1 deletion docs/user_guide/nodes/matrix/combine_matrices.rst
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Expand Up @@ -3,7 +3,7 @@ Combine Matrices

Description
-----------
This takes a list of transformation matrices and multiply them together in order.
This takes a list of transformation matrices and performs them together in order.

.. image:: images/combine_matrices_node.png
:width: 160pt
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2 changes: 1 addition & 1 deletion docs/user_guide/nodes/matrix/compose_matrix.rst
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Expand Up @@ -3,7 +3,7 @@ Decompose Matrix

Description
-----------
This node forms a 4x4 transformation matrix based on input translation,rotation and scalling.
This node forms a 4x4 transformation matrix based on input translation, rotation, and scalling.

.. image:: images/compose_matrix_node.png
:width: 160pt
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22 changes: 11 additions & 11 deletions docs/user_guide/nodes/matrix/decompose_matrix.rst
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Expand Up @@ -12,29 +12,29 @@ rotation, translation and scale.
Demonstration
-------------

In CG applications object's location, rotation and scale are stored in what is
In CG applications object's location, rotation, and scale are stored in what is
knows as the **Homogeneous Coordinates Transformation Matrix**.

**Homogeneous Coordinates Transformation Matrix** is a 4x4 matrix where the rotation
information is stored in the initial 3x3 matrix, location information stored in the
first 3 rows of the last column and scale information stored in the diagonal of
the initial 3x3 matrix.

To rotate, translate or scale this object or point, you have to edit this 4x4 matrix
To rotate, translate, or scale this object or point, you must edit this 4x4 matrix
in a special way.

To rotate the point you have to multiply the matrix by a special matrix called
the **Rotation Transformation Matrix**, and this multiplication will result a
To rotate the point you must multiply the matrix by a special matrix called
the **Rotation Transformation Matrix**, and this multiplication will result in a
new matrix representing the rotated point which is the the same as the original
matrix but with the initial 3x3 matrix changed.

To translate the point you have to multiply the matrix by a special matrix called
the **Translation Transformaton Matrix**, and this multiplication will result a
To translate the point you must multiply the matrix by a special matrix called
the **Translation Transformaton Matrix**, and this multiplication will result in a
new matrix representing the translated point which is the same as the original
matrix but with the first 3 rows of the last column changed.

To scale the point you have to multiply the matrix by a special matrix called
the **Scaling Transformation Matrix**, and this multiplication will result a new
To scale the point you must multiply the matrix by a special matrix called
the **Scaling Transformation Matrix**, and this multiplication will result in a new
matrix representing the scalled point which is the same as the original matrix
but with the diagonal of the initial 3x3 matrix amplified by a specific factor.

Expand All @@ -56,13 +56,13 @@ Outputs
-------

- **Translation**
A vector that store the amount of translation in the input matrix, which is
A vector that stores the amount of translation in the input matrix, which is
also the location of the object.
- **Rotation**
An euler that store the amount of rotation in the input matrix, which is
An euler that stores the amount of rotation in the input matrix, which is
also the rotation of the object.
- **Scale**
A vector that store the amount of scalling in the input matrix, which is
A vector that stores the amount of scalling in the input matrix, which is
also the scale of the object.

Advanced Node Settings
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4 changes: 2 additions & 2 deletions docs/user_guide/nodes/matrix/invert_matrix.rst
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Expand Up @@ -3,8 +3,8 @@ Invert Matrix

Description
-----------
This node invert the input transformation matrix.
In other words, this node will return a matrix that reverse the effect of the input matrix.
This node inverts the input transformation matrix.
In other words, this node will return a matrix that reverses the effect of the input matrix.

.. image:: images/invert_matrix_node.png
:width: 160pt
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8 changes: 4 additions & 4 deletions docs/user_guide/nodes/matrix/matrix_math.rst
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Expand Up @@ -3,13 +3,13 @@ Matrix Math

Description
-----------
This node enable you to multiple 2 transformation matrices.
This node aloows you to multiply 2 transformation matrices.
Multiplying transformation matrices gets you a transformation matrix that will
perform all the input transformation matrices. So if you multiplied a rotation
matrix by a translation matrix the reslted matrix is a transformation matrix that
perform rotation then translation.
matrix by a translation matrix the resultant matrix is a transformation matrix that
performs rotation and then translation.

Put in mind that matrix multiplication is non commutative.
Keep in mind that matrix multiplication is non commutative.

.. image:: images/matrix_math_node.png
:width: 160pt
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