TransformationMatrix functions

[XANCI]

Scale x by a, y by b based point (x,y)

Code: Select all

function Scale(x,y,a,b)
	local t={a,0,0,b,(1-a)*x,(1-b)*y}
	return t
end

Rotate r(radian) around point (x,y)

Code: Select all

function Rotate(x,y,r)
	local t={math.cos(r),math.sin(r),-math.sin(r),math.cos(r),x*(1-math.cos(r))+y*math.sin(r),y*(1-math.cos(r))-x*math.sin(r)}
	return t
end

Multiply matrix a by b

Code: Select all

function Multiply(a,b)
	local t={}
	t[1]=a[1]*b[1]+a[2]*b[3]
	t[2]=a[1]*b[2]+a[2]*b[4]
	t[3]=a[3]*b[1]+a[4]*b[3]
	t[4]=a[3]*b[2]+a[4]*b[4]
	t[5]=a[5]*b[1]+a[6]*b[3]+b[5]
	t[6]=a[5]*b[2]+a[6]*b[4]+b[6]
	return t
end

Output a matrix as a string used by TransformationMatrix

Code: Select all

function Ouput(t)
	local s=t[1]..';'..t[2]..';'..t[3]..';'..t[4]..';'..t[5]..';'..t[6]
	return s
end

Example:
Scale both x&y by 2 and rotate 90 degree around (100,100)

Code: Select all

TM0={1,0,0,1,0,0}
TM1=Scale(100,100,2,2)
TM2=Rotate(100,100,math.pi/4)
TM=Multiply(Multiply(iTM0,iTM1),iTM2)
SKIN:Bang('!SetOption','Meter','TransformationMatrix',Output(TM))

[smurfier]

Output a matrix as a string used by TransformationMatrix

Code: Select all

function Ouput(t)
	local s=t[1]..';'..t[2]..';'..t[3]..';'..t[4]..';'..t[5]..';'..t[6]
	return s
end

Code: Select all

function Ouput(t)
	return table.concat(t, ';')
end

Also, if you set your matrices up a bit different, this function will multiply them regardless of size as long as the columns in matrixA equals the rows in matrixB.

Code: Select all

matrixA = {
	{1,0,0},
	{0,1,0},
	{0,0,1},
}

matrixB = {
	{0,0,1},
	{0,1,0},
	{1,0,0},
}

function Multiply(tbl1, tbl2)
	local temp = {}
	for row = 1, #tbl1 do
		temp[row] = {}
		for col = 1, #tbl2[1] do
			local num = 0
			for row2 = 1, #tbl1[1] do
				num = num + tbl1[row][row2] * tbl2[row][col]
			end
			temp[row][col] = num
		end
	end
	return temp
end

[MerlinTheRed]

Can you give an example of how one might use this in a skin? I imagine the uses cases are rather complex, but probably I'm wrong.

I think it might be even more useful to have a Lua script that creates a TransformationMatrix from simple, user-understandable parameters like rotation angle, translation and scale. Of course the space of all possible transformations would not be completely represented by this but it will enable not-so-math-savvy users to use TransformationMatrix.

[Unight]

Code: Select all

function Ouput(t)
	return table.concat(t, ';')
end

Also, if you set your matrices up a bit different, this function will multiply them regardless of size as long as the columns in matrixA equals the rows in matrixB.

Code: Select all

matrixA = {
	{1,0,0},
	{0,1,0},
	{0,0,1},
}

matrixB = {
	{0,0,1},
	{0,1,0},
	{1,0,0},
}

function Multiply(tbl1, tbl2)
	local temp = {}
	for row = 1, #tbl1 do
		temp[row] = {}
		for col = 1, #tbl2[1] do
			local num = 0
			for row2 = 1, #tbl1[1] do
				num = num + tbl1[row][row2] * tbl2[row][col]
			end
			temp[row][col] = num
		end
	end
	return temp
end

This function is more Interesting.