Vector Math Object
From FusionWiki
| Vector Math Object | |
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| General Information | |
| Author: | Justin Aquadro |
| Release Date: | 2010 |
| Status: | Released |
| Last updated: | Unknown |
| Version: | 1.0 |
| Build: | |
| Developer-only: | No |
| Website: | Not available |
| Download: | Direct |
| Runtime Versions | |
| HWA: | Yes |
| Flash: | No |
| Java: | No |
| Java Mobile: | No |
| Vitalize!: | No |
| Unicode: | No |
The Vector Math Object supports an assortment of operations on vectors and transpose-vectors of length 2, 3, and 4, and on square matrices of size 3 and 4.
Each object can store an unlimited number of vectors, transpose-vectors, and matrices, each identified by a unique string. Each operation will accept one or more source vectors/matrices, and return the result into a separate result vector/matrix (which can be the same as one of the sources). Several predefined vectors and matrices are available such as unit vectors and the zero and identity matrices.
Contents |
Vector Operations
Vector Definition
- Set Vector from Values
- Set Vector from Vector
- Set Vector element
Vector Math
- Add Vector (V1 = V2 + V3)
- Add Constant (V1 = V2 + C1)
- Subtract Vector (V1 = V2 - V3)
- Subtract Constant (V1 = V2 - C1)
- Scale (V1 = V2 * C1)
- Scale-Add (V1 = V2 * C1 + C2)
- Negate (V1 = 0 - V2)
- Absolute Value (For e in V1, V2[] = |e|)
- Clamp Values (For e in V1, V2[] = max(C1, min(C2, e)))
- Clamp Maximum Values (For e in V1, V2[] = min(C1, e))
- Clamp Minimum Values (For e in V1, V2[] = max(C1, e))
- Cross Product (V1 = V2 ⨯ V3)
- Normalize (For e in V1, V2[] = e / max(V1))
- Transpose (V1T = V2T)
Vector Expressions
- Dot Product (expr = V1 · V2)
- Angle (expr = acos(V1 · V2 / |V1||V2|))
- Length (expr = |V1|)
- Length Squared (expr = |V1|2)
- Multiply Transpose-Vector and Vector (expr = V1T * V2)
Matrix Operations
Matrix Definition
- Set Matrix from Vectors
- Set Matrix from Matrix
- Set Matrix Row from Values
- Set Matrix Row from Vector
- Set Matrix Column from Values
- Set Matrix Column from Vector
- Set Matrix Element
Matrix Math
- Add Matrix (M1 = M2 + M3)
- Add Constant (M1 = M2 + C1)
- Subtract Matrix (M1 = M2 - M3)
- Subtract Constant (M1 = M2 - C1)
- Multiply Matrix (M1 = M2 * M3)
- Multiply Constant (M1 = M2 * C1)
- Multiply Matrix and Vector (M1 = M2 * V1)
- Multiply Transpose-Vector and Matrix (M1 = V1T * M2)
- Negate (M1 = 0 - M2)
- Invert (M1 = M2-1)
- Transpose (M1 = M2T)
- 3D Operations on 4x4 Matrices
- Rotate
- Rotate on X-Axis
- Rotate on Y-Axis
- Rotate on Z-Axis
- Scale
- Translate
Matrix Expressions
- Determinant (expr = det(M1))
Usage
The following usage shows part of the Forward Kinematics example, where matrix operations are used to propagate translations and rotations of connected links, so that each link in the chain is affected by the translation and rotation of all the links before it. Position values are then read from the matrices TransG0, TransG1, etc. to update the positions of corresponding links.
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