https://community.graphisoft.com/t5/Libraries-objects/mathematical-problem-coordinate-transform/m-p/115928#M27695 Just look <A href="http://en.wikipedia.org/wiki/Transformation_matrix" target="_blank">here</A> at the affine transformations<BR /> <BR /> If you want to remember it EVERY time here it is how you figure it out<BR /> <BR /> the basic vectors are ex(1,0) ey(0,1) and if you rotate it by angle a the new vectors are ex'(cosa,sina) ey'(-sina,cosa). To figure out the new coordinates just draw the trigonometric cycle and you will find easily the new coordinates (unfortunately i cannot draw it here)<BR /> <BR /> Now the matrix<BR /> <BR /> | a1 a2 | <BR /> | |*ex = ex' from there you have a1 and a3 and from<BR /> | a3 a4 |<BR /> <BR /> | a1 a2 | <BR /> | |*ey = ey' from there you have a2 and a2<BR /> | a3 a4 |<BR /> <BR /> basically if you name ex'T the transposed ex' vector (make the row a column) then<BR /> <BR /> A = |ex'T ey'T| Thu, 19 Jun 2008 10:47:45 GMT Anonymous 2008-06-19T10:47:45Z https://community.graphisoft.com/t5/Libraries-objects/mathematical-problem-coordinate-transform/m-p/115927#M27694 <DIV class="actalk-migrated-content"><T>Hello...<BR /> <BR /> Can anybody please help me with a mathematical problem?<BR /> <BR /> I'm trying to transform (2D) the coordinates of a point from one coordinate system to another.<BR /> <BR /> I know there are equations for that but I can't find them...<BR /> <BR /> Thank you in advance</T></DIV> Thu, 19 Jun 2008 09:34:40 GMT https://community.graphisoft.com/t5/Libraries-objects/mathematical-problem-coordinate-transform/m-p/115927#M27694 Anonymous 2008-06-19T09:34:40Z https://community.graphisoft.com/t5/Libraries-objects/mathematical-problem-coordinate-transform/m-p/115928#M27695 Just look <A href="http://en.wikipedia.org/wiki/Transformation_matrix" target="_blank">here</A> at the affine transformations<BR /> <BR /> If you want to remember it EVERY time here it is how you figure it out<BR /> <BR /> the basic vectors are ex(1,0) ey(0,1) and if you rotate it by angle a the new vectors are ex'(cosa,sina) ey'(-sina,cosa). To figure out the new coordinates just draw the trigonometric cycle and you will find easily the new coordinates (unfortunately i cannot draw it here)<BR /> <BR /> Now the matrix<BR /> <BR /> | a1 a2 | <BR /> | |*ex = ex' from there you have a1 and a3 and from<BR /> | a3 a4 |<BR /> <BR /> | a1 a2 | <BR /> | |*ey = ey' from there you have a2 and a2<BR /> | a3 a4 |<BR /> <BR /> basically if you name ex'T the transposed ex' vector (make the row a column) then<BR /> <BR /> A = |ex'T ey'T| Thu, 19 Jun 2008 10:47:45 GMT https://community.graphisoft.com/t5/Libraries-objects/mathematical-problem-coordinate-transform/m-p/115928#M27695 Anonymous 2008-06-19T10:47:45Z