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Using SetWorldTransform() to rotate basic shapes by any angle

, 24 Feb 2002
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How to use SetWorldTransform() to draw basic shapes rotated by any angle

Introduction

MFC provides many functions to draw basic shapes, such as rectangle, ellipse, polygon, etc. It’s just a piece of cake. Also, a rectangle rotated 45 degrees can be drawn easily after doing a little math. But what if we want to rotate these shapes to a weird angle, say 11 degrees? Or we want to rotate an ellipse by 37 degrees?

Use SetWorldTransform() can free you from all the mathematics.

Details

First of all, let’s review the definition of rotation: the rotation performs a geometric transform which maps the position (x1, y1) of a picture element in an input image onto a position (x2, y2) in an output image by rotating it through a user-specified angle q about an origin (x0, y0).

The formula is:

    x2 = cos(q)*(x1-x0) – sin(q)*(y1-y0) + x0;
    y2 = sin(q)*(x1-x0) + cos(q)*(y1-y0) + y0; // ------ (1)

where (x0, y0) are the coordinates of the center of rotation (in the input image) and q is the angle of rotation with clockwise rotations having positive angles.

Note here that we are working in image coordinates, so the y axis goes downward. With above formulas in mind, let’s check what SetWorldTransform() can do for us.

From MSDN, it’s said that using SetWorldTransform(), for any coordinates (x, y) in world space, the transformed coordinates in page space (x’, y’) can be determined by the following algorithm:

    x’ = x * eM11 + y * eM12 + eDx;
    y’ = x * eM12 + y * eM22 + eDy; // ------ (2)

Compare these two groups of formulas, we can get the correct values for parameter xform:

    xform.eM11 = cos(q);
    xform.eM12 = sin(q);
    xform.eM21 = -sin(q);
    xform.eM22 = cos(q);
    xform.eDx = x0 – cos(q)*x0 + sin(q)*y0;
    xform.eDy = y0 – cos(q)*y0 - sin(q)*x0;

That’s all the myth. Included is a simple project to demonstrate it.

License

This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.

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About the Author

lucy
Software Developer
Canada Canada
I love this place!

Comments and Discussions

 
NewsHelping me eleven years later! PinmemberAlasdair Craig4-Sep-13 8:44 
GeneralOutstanding! Good suppliment to the MFC docs PinmemberBruff16-Mar-11 5:02 
GeneralRotating bitmap with any angle with out usinf MFC Pinmemberswethakiran3-Feb-08 17:31 
GeneralAmazing, but isn't it a little obvious PinmemberArtiBen25-Jun-07 3:52 
Generalcode to change orientation. Pinmemberchinesepatriotleague30-May-07 19:33 
GeneralThank you so much! Pinmemberfreeman86827-Mar-07 21:17 
QuestionWhat is the Logic behind the API CreateRoundRectRgn() or code Pinmemberprabhashmandal18-Aug-06 3:10 
GeneralCombine with scaling... PinmemberRYU^^9-Oct-05 4:37 
GeneralRe: Combine with scaling... PinmemberArtiBen25-Jun-07 3:54 
GeneralWinCE Equivalent PinmemberMeenu_Sachdeva23-May-05 5:26 
GeneralVery good! Pinmemberandystone6-May-05 19:48 
GeneralPrint Pinmemberbitmensch13-Feb-05 22:51 
GeneralSeries of circles PinmemberJolyn13-Dec-03 14:37 
GeneralIt can't work for Windows 95/98/Me PinmemberDanney15-Apr-03 22:26 
GeneralRe: It can't work for Windows 95/98/Me Pinmemberjdunlap26-Sep-03 10:06 
GeneralI need to rotate the whole form (A graphical editor) PinmemberDhirendra10-Mar-03 2:32 
GeneralRe: I need to rotate the whole form (A graphical editor) PinmemberBarty791-Jul-05 5:03 
GeneralRe: I need to rotate the whole form (A graphical editor) PinmemberDhirendra3-Jul-05 20:00 
Generalresizing and moving images as in Word Art Pinmembersreemail13-Dec-02 23:24 
GeneralRe: resizing and moving images as in Word Art PinmemberArtiBen25-Jun-07 3:58 
GeneralNice! But show the posibilities! :) PinmemberLars [Large] Werner13-Dec-02 9:41 
GeneralNice description and demonstration PinmemberShog95-Mar-02 6:08 

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