CODEWITHSUNDEEP
geometrytransform
Max
Max

Reputation: 8045

transform point to another coordinate

suggest here are 3 points on,(x0,y0),(x1,y1),(x2,y2)

O = (x0,y0)
e1 = (x1-x0,y1-y0)
e2 = (x2-x0,y2-y0)

3 can make a new cordinate (O,e1,e2)

here's a point (x,y)

how to calculate the point location in (O,e1,e2)?please write down the formula ,thanks.

once i remember,but now i forget.

Upvotes: 0

Views: 411

Answers (1)

maxim1000
maxim1000

Reputation: 6365

Let's call new coordinates a and b.

In the old coordinate system the point will be O+a*e1+b*e2. Since it should be the same point (x,y), we have two linear equations:

x=Ox+a*e1x+b*e2x
y=Oy+a*e1y+b*e2y

Everything except a and b is known, two unknowns, two equations - solution exists if e1 and e2 are not parallel.

The system can be solved either by inversion of matrix ( (e1x,e2x) , (e1y,e2y) ), or by expressing a in terms of b from the first equation and substituting it into the second one.

Upvotes: 2

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