1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
|
<?xml version="1.0" encoding="UTF-8" ?>
<class name="Basis" version="4.0">
<brief_description>
3×3 matrix datatype.
</brief_description>
<description>
3×3 matrix used for 3D rotation and scale. Almost always used as an orthogonal basis for a Transform.
Contains 3 vector fields X, Y and Z as its columns, which are typically interpreted as the local basis vectors of a transformation. For such use, it is composed of a scaling and a rotation matrix, in that order (M = R.S).
Can also be accessed as array of 3D vectors. These vectors are normally orthogonal to each other, but are not necessarily normalized (due to scaling).
For more information, read the "Matrices and transforms" documentation article.
</description>
<tutorials>
<link title="Math tutorial index">https://docs.godotengine.org/en/latest/tutorials/math/index.html</link>
<link title="Matrices and transforms">https://docs.godotengine.org/en/latest/tutorials/math/matrices_and_transforms.html</link>
<link title="Using 3D transforms">https://docs.godotengine.org/en/latest/tutorials/3d/using_transforms.html</link>
<link title="Matrix Transform Demo">https://godotengine.org/asset-library/asset/584</link>
<link title="3D Platformer Demo">https://godotengine.org/asset-library/asset/125</link>
<link title="3D Voxel Demo">https://godotengine.org/asset-library/asset/676</link>
<link title="2.5D Demo">https://godotengine.org/asset-library/asset/583</link>
</tutorials>
<methods>
<method name="Basis" qualifiers="constructor">
<return type="Basis">
</return>
<description>
Constructs a default-initialized [Basis] set to [constant IDENTITY].
</description>
</method>
<method name="Basis" qualifiers="constructor">
<return type="Basis">
</return>
<argument index="0" name="from" type="Basis">
</argument>
<description>
Constructs a [Basis] as a copy of the given [Basis].
</description>
</method>
<method name="Basis" qualifiers="constructor">
<return type="Basis">
</return>
<argument index="0" name="axis" type="Vector3">
</argument>
<argument index="1" name="phi" type="float">
</argument>
<description>
Constructs a pure rotation basis matrix, rotated around the given [code]axis[/code] by [code]phi[/code], in radians. The axis must be a normalized vector.
</description>
</method>
<method name="Basis" qualifiers="constructor">
<return type="Basis">
</return>
<argument index="0" name="euler" type="Vector3">
</argument>
<description>
Constructs a pure rotation basis matrix from the given Euler angles (in the YXZ convention: when *composing*, first Y, then X, and Z last), given in the vector format as (X angle, Y angle, Z angle).
Consider using the [Quat] constructor instead, which uses a quaternion instead of Euler angles.
</description>
</method>
<method name="Basis" qualifiers="constructor">
<return type="Basis">
</return>
<argument index="0" name="from" type="Quat">
</argument>
<description>
Constructs a pure rotation basis matrix from the given quaternion.
</description>
</method>
<method name="Basis" qualifiers="constructor">
<return type="Basis">
</return>
<argument index="0" name="x_axis" type="Vector3">
</argument>
<argument index="1" name="y_axis" type="Vector3">
</argument>
<argument index="2" name="z_axis" type="Vector3">
</argument>
<description>
Constructs a basis matrix from 3 axis vectors (matrix columns).
</description>
</method>
<method name="determinant">
<return type="float">
</return>
<description>
Returns the determinant of the basis matrix. If the basis is uniformly scaled, its determinant is the square of the scale.
A negative determinant means the basis has a negative scale. A zero determinant means the basis isn't invertible, and is usually considered invalid.
</description>
</method>
<method name="get_euler">
<return type="Vector3">
</return>
<description>
Returns the basis's rotation in the form of Euler angles (in the YXZ convention: when decomposing, first Z, then X, and Y last). The returned vector contains the rotation angles in the format (X angle, Y angle, Z angle).
Consider using the [method get_rotation_quat] method instead, which returns a [Quat] quaternion instead of Euler angles.
</description>
</method>
<method name="get_orthogonal_index">
<return type="int">
</return>
<description>
This function considers a discretization of rotations into 24 points on unit sphere, lying along the vectors (x,y,z) with each component being either -1, 0, or 1, and returns the index of the point best representing the orientation of the object. It is mainly used by the [GridMap] editor. For further details, refer to the Godot source code.
</description>
</method>
<method name="get_rotation_quat">
<return type="Quat">
</return>
<description>
Returns the basis's rotation in the form of a quaternion. See [method get_euler] if you need Euler angles, but keep in mind quaternions should generally be preferred to Euler angles.
</description>
</method>
<method name="get_scale">
<return type="Vector3">
</return>
<description>
Assuming that the matrix is the combination of a rotation and scaling, return the absolute value of scaling factors along each axis.
</description>
</method>
<method name="inverse">
<return type="Basis">
</return>
<description>
Returns the inverse of the matrix.
</description>
</method>
<method name="is_equal_approx">
<return type="bool">
</return>
<argument index="0" name="b" type="Basis">
</argument>
<description>
Returns [code]true[/code] if this basis and [code]b[/code] are approximately equal, by calling [code]is_equal_approx[/code] on each component.
</description>
</method>
<method name="operator !=" qualifiers="operator">
<return type="bool">
</return>
<argument index="0" name="right" type="Basis">
</argument>
<description>
</description>
</method>
<method name="operator *" qualifiers="operator">
<return type="Vector3">
</return>
<argument index="0" name="right" type="Vector3">
</argument>
<description>
</description>
</method>
<method name="operator *" qualifiers="operator">
<return type="Basis">
</return>
<argument index="0" name="right" type="Basis">
</argument>
<description>
</description>
</method>
<method name="operator ==" qualifiers="operator">
<return type="bool">
</return>
<argument index="0" name="right" type="Basis">
</argument>
<description>
</description>
</method>
<method name="operator []" qualifiers="operator">
<return type="Vector3">
</return>
<argument index="0" name="index" type="int">
</argument>
<description>
</description>
</method>
<method name="orthonormalized">
<return type="Basis">
</return>
<description>
Returns the orthonormalized version of the matrix (useful to call from time to time to avoid rounding error for orthogonal matrices). This performs a Gram-Schmidt orthonormalization on the basis of the matrix.
</description>
</method>
<method name="rotated">
<return type="Basis">
</return>
<argument index="0" name="axis" type="Vector3">
</argument>
<argument index="1" name="phi" type="float">
</argument>
<description>
Introduce an additional rotation around the given axis by phi (radians). The axis must be a normalized vector.
</description>
</method>
<method name="scaled">
<return type="Basis">
</return>
<argument index="0" name="scale" type="Vector3">
</argument>
<description>
Introduce an additional scaling specified by the given 3D scaling factor.
</description>
</method>
<method name="slerp">
<return type="Basis">
</return>
<argument index="0" name="b" type="Basis">
</argument>
<argument index="1" name="t" type="float">
</argument>
<description>
Assuming that the matrix is a proper rotation matrix, slerp performs a spherical-linear interpolation with another rotation matrix.
</description>
</method>
<method name="tdotx">
<return type="float">
</return>
<argument index="0" name="with" type="Vector3">
</argument>
<description>
Transposed dot product with the X axis of the matrix.
</description>
</method>
<method name="tdoty">
<return type="float">
</return>
<argument index="0" name="with" type="Vector3">
</argument>
<description>
Transposed dot product with the Y axis of the matrix.
</description>
</method>
<method name="tdotz">
<return type="float">
</return>
<argument index="0" name="with" type="Vector3">
</argument>
<description>
Transposed dot product with the Z axis of the matrix.
</description>
</method>
<method name="transposed">
<return type="Basis">
</return>
<description>
Returns the transposed version of the matrix.
</description>
</method>
</methods>
<members>
<member name="x" type="Vector3" setter="" getter="" default="Vector3( 1, 0, 0 )">
The basis matrix's X vector (column 0). Equivalent to array index [code]0[/code].
</member>
<member name="y" type="Vector3" setter="" getter="" default="Vector3( 0, 1, 0 )">
The basis matrix's Y vector (column 1). Equivalent to array index [code]1[/code].
</member>
<member name="z" type="Vector3" setter="" getter="" default="Vector3( 0, 0, 1 )">
The basis matrix's Z vector (column 2). Equivalent to array index [code]2[/code].
</member>
</members>
<constants>
<constant name="IDENTITY" value="Basis( 1, 0, 0, 0, 1, 0, 0, 0, 1 )">
The identity basis, with no rotation or scaling applied.
This is identical to calling [code]Basis()[/code] without any parameters. This constant can be used to make your code clearer, and for consistency with C#.
</constant>
<constant name="FLIP_X" value="Basis( -1, 0, 0, 0, 1, 0, 0, 0, 1 )">
The basis that will flip something along the X axis when used in a transformation.
</constant>
<constant name="FLIP_Y" value="Basis( 1, 0, 0, 0, -1, 0, 0, 0, 1 )">
The basis that will flip something along the Y axis when used in a transformation.
</constant>
<constant name="FLIP_Z" value="Basis( 1, 0, 0, 0, 1, 0, 0, 0, -1 )">
The basis that will flip something along the Z axis when used in a transformation.
</constant>
</constants>
</class>
|