GLM: How to create a matrix of 9 columns and 3 rows

Question

I know only one way which is glm::mat4 matrix

I tried even float matrix[9][3] which didn't work, I need it to multiply it with glm::vec3

How to create?

Answer 1

You can compute that with 3x3 sub matrices and combine the outputs into final result. There are two options:

1. 9 rows

    a a a       u'
    a a a       u'
    a a a       u'
    b b b   u   v'
    b b b * u = v'
    b b b   u   v'
    c c c       w'
    c c c       w'
    c c c       w'
   

   this is really simple:

    u' = a*u
    v' = b*u
    w' = c*u
   

2. 9 columns

                        u
                        u
                        u
    a a a b b b c c c   v   u' 
    a a a b b b c c c * v = u'
    a a a b b b c c c   v   u'
                        w
                        w
                        w
   

This is more complicated but not by much:

    u.x' = (a*u).x + (b*v).x + (c*w).x
    u.y' = (a*u).y + (b*v).y + (c*w).y
    u.z' = (a*u).z + (b*v).z + (c*w).z

This is common way for expanding dimensionality in GLSL for example for purposes like these:

• 4D rendering
• 4D rotations

[Edit1] 9x3 and 3x9 matrices version:

+-----+                         +-----------------+
|     |                         |     |     |     |
|  A  |                         | A*U | A*V | A*W |
|     |                         |     |     |     |
|-----|   +-----------------+   |-----+-----+-----|
|     |   |     |     |     |   |     |     |     |
|  B  | * |  U  |  V  |  W  | = | B*U | B*V | B*W |
|     |   |     |     |     |   |     |     |     |
|-----|   +-----------------+   |-----+-----+-----|
|     |                         |     |     |     |
|  C  |                         | C*U | C*V | C*W |
|     |                         |     |     |     |
+-----+                         +-----------------+

                               +--------+
                               |u1 u2 u3|
                               |u1 u2 u3|
                               |u1 u2 u3|
+--------------------------+   |--------|   +-----------------------------------------------------------------------------+
|a1 a1 a1|b1 b1 b1|c1 c1 c1|   |v1 v2 v3|   | (a1.u1)+(b1.v1)+(c1.w1) | (a1.u2)+(b1.v2)+(c1.w2) | (a1.u3)+(b1.v3)+(c1.w3) |
|a2 a2 a2|b2 b2 b2|c2 c2 c2| * |v1 v2 v3| = | (a2.u1)+(b2.v1)+(c2.w1) | (a2.u2)+(b2.v2)+(c2.w2) | (a2.u3)+(b2.v3)+(c2.w3) |
|a3 a3 a3|b3 b3 b3|c3 c3 c3|   |v1 v2 v3|   | (a3.u1)+(b3.v1)+(c3.w1) | (a3.u2)+(b3.v2)+(c3.w2) | (a3.u3)+(b3.v3)+(c3.w3) |
+--------------------------+   |--------|   +-----------------------------------------------------------------------------+
                               |w1 w2 w3|
                               |w1 w2 w3|
                               |w1 w2 w3|
                               +--------+

where (a1.u1) means dot product between (a1,a1,a1) and (u1,u1,u1) and uppercase A means entire 3x3 submatrix