Point / Matrix multiplication

I have a 3-dimensional point and a 4x4 matrix.

How do I multiply the point by the matrix to push it "into" the matrix (transform from world to this matrix)?

How do I transform the point from the matrice's space to the world?

Why have you got a 4x4 matrix?

It's one better.

are you asking how to do vector+matrix multiplication or how to be able to construct inverse matrices to transform a point from global to local coordinates and vice versa?

For starters, matrix multiplication is not defined for two matrices of 3-by-1 and 4-by-4 sizes.

This is a technical trick so that matrix multiplication can move a vector to a new location.
The idea is to encode a 3-d vector (x,y,z) into 4-d as (x,y,z,1).

If you worked only in 3-d then matrix*vector would always leave the zero vector (0,0,0) unchanged.

The exact details depend on what convention is used.
The vector may be considered as a row and the multiplication is vector*matrix
Or the vector may be a column and you do matrix*vector.

I think Direct3D uses the first approach and OpenGL uses the second.

I found that if I created a matrix from the position and multiplied it by the other, I could get the transformed position.

To get "out" of a matrix, I used the inverse matrix.

Here's how I did TFormPoint():

Function TFormPoint(x#,y#,z#,src_ent:TEntity,dest_ent:TEntity)
	If dest_ent
		If Not dest_ent.mat dest_ent=Null
	EndIf
	
	Local mat:TMatrix=New TMatrix
	Local mat2:TMatrix
	
	If src_ent
		mat2=src_ent.mat.copy()
		mat=TMatrix.FromPoint(vec3(x,y,z))
		mat2.multiply(mat)
		x=mat2.grid[3,0]
		y=mat2.grid[3,1]
		z=mat2.grid[3,2]
	EndIf
	
	If dest_ent
		mat2=dest_ent.mat.inverse()
		mat=TMatrix.FromPoint(vec3(x,y,z))
		mat2.multiply(mat)
		x=mat2.grid[3,0]
		y=mat2.grid[3,1]
		z=mat2.grid[3,2]
	EndIf
	
	tformed_x#=x#
	tformed_y#=y#
	tformed_z#=z#
EndFunction

To do a vector, you just set the entity matrix position to 0.

Looks like you got it sorted, looks almost exactly like what I had (except, I'm using Ogre's methods.)

I recently got into this matrix stuff myself. It was a pain for a starter because looking around it was rather difficult to find what to multiply with what. Thanks for sharing your solution- two months ago this would have saved me quite a long time googling and I'm sure others will find it useful. :-)