Rotation - Win32 Programmer's Reference

Custom Search

Rotation

Many CAD applications provide features that rotate objects drawn in the client area. If your application features rotation capabilities, use the SetWorldTransform function to set the appropriate world-space to page-space transformation. This function receives a pointer to an XFORM structure containing the appropriate values. The eM11, eM12, eM21, and eM22 members of XFORM specify, respectively, the cosine, sine, negative sine, and cosine of the angle of rotation.

When rotation occurs, the points that constitute an object are rotated with respect to the coordinate-space origin. The following illustration shows a 20- by 20-unit rectangle rotated 30 degrees when copied from world coordinate space to page coordinate space.

In the preceding illustration, each point in the rectangle was rotated 30 degrees with respect to the coordinate-space origin.

The following algorithm computes the new x-coordinate (x') for a point (x,y) that is rotated by angle A with respect to the coordinate-space origin.

x' = (x * cos A) - (y * sin A)

The following algorithm computes the y-coordinate (y') for a point (x,y) that is rotated by the angle A with respect to the origin.

y' = (x * sin A) + (y * cos A)

The two rotation transformations can be combined in a 2-by-2 matrix as follows.

|x' y'| == |x y| * | cos A sin A|

|-sin A cos A|

The 2-by-2 matrix that produced the rotation contains the following values.

| .8660 .5000|

|-.5000 .8660|

Rotation Algorithm Derivation
Rotation algorithms are based on trigonometry's addition theorem stating that the trigonometric function of a sum of two angles (A1 and A2) can be expressed in terms of the trigonometric functions of the two angles.

sin(A1 + A2) = (sin A1 * cos A2) + (cos A1 * sin A2)

cos(A1 + A2) = (cos A1 * cos A2) - (sin A1 * sin A2)

The following illustration shows a point p rotated counterclockwise to a new position p'. In addition, it shows two triangles formed by a line drawn from the coordinate-space origin to each point and a line drawn from each point through the x-axis.

Using trigonometry, the x-coordinate of point p can be obtained by multiplying the length of the hypotenuse h by the cosine of A1.

x = h * cos A1

The y-coordinate of point p can be obtained by multiplying the length of the hypotenuse h by the sine of A1.

y = h * sin A1

Likewise, the x-coordinate of point p' can be obtained by multiplying the length of the hypotenuse h by the cosine of (A1 + A2).

x' = h * cos (A1 + A2)

Finally, the y-coordinate of point p' can be obtained by multiplying the length of the hypotenuse h by the sine of (A1 + A2).

y' = h * sin (A1 + A2)

Using the addition theorem, the preceding algorithms become the following.

x' = (h * cos A1 * cos A2) - (h * sin A1 * sin A2)

y' = (h * cos A1 * sin A2) + (h * sin A1 * cos A2)

The rotation algorithms for a given point rotated by angle A2 can be obtained by substituting x for each occurrence of (h * cos A1) and substituting y for each occurrence of (h * sin A1).

x' = (x * cos A2) - (y * sin A2)

y' = (x * sin A2) + (y * cos A2)

Last news from Greatis Software

    Nostalgia .Net     .Net is powerful, but not all-powerful, so sometimes we need to use Win32 API for our .Net applications. It's simple enough with Platform Invoke if you have Win32 skill, but we do not always have time to dig the ancient documentation, declare the special types that are compatible with Win32, find the values of the Win32's constants and so on. Nostalgia .Net offers several simple-to-use classes, and components that will allow you to forget about the headache of Win32 and just use the power of Win32 in your application the same way as you use the native. Net classes. More »

Recommended software for developers

    Ultimate Pack     Component pack for Delphi and C++ Builder that contains runtime form designer, runtime object inspector, print suite and much more for the very special price. More »

    Form Designer .Net     Unique runtime form design solution that allows to edit any form in .Net WinForms application at runtime with full source codes for only 300 euro! More »

    Print Suite .Net     Print Suite .Net is a set of components for easy printing texts, images and grids from your WinForms applications. Full C# source codes are available More »

    Gradient Controls .Net     Gradient Controls .Net offers controls with gradient background feature. Labels, panels and so on... Full C# source codes are available More »

    Greatis iGrid     iGrid plots drawing grid right over your desktop, so you can use it everywhere, with any drawing application without any special plugins for different graphic editors. More »

All the contacts and projects

Dmitry Vasiliev (just.dmitry)

More Online Helps

Win32 Programmer's Reference
Win32 Multimedia Programmer's Reference
OLE Programmer's Reference
Microsoft Windows Pen API Programmer's Reference
Microsoft Windows Sockets 2 Reference
Microsoft Windows Telephony API (TAPI) Programmer's Reference
Unix Manual Pages

greatis just4fun network