Using SetWorldTransform() to rotate basic shapes by any angle

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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.