Coordinate Spaces and Transformations

Coordinate Spaces and Transformations

Applications use coordinate spaces and transformations to scale, rotate, translate, shear, and reflect graphics output. Acoordinate space is a planar space that locates two-dimensional objects by using two reference axes that are perpendicular to each other. There are four coordinate spaces: world, page, device, and physical device (client area, desktop, or page of printer paper).

A transformation is an algorithm that alters ("transforms") the size, orientation, and shape of objects. Transformations also transfer a graphics object from one coordinate space to another. Ultimately, the object appears on the physical device, which is usually a screen or printer.

一个例子：

Using Coordinate Spaces and Transformations

This section contains an example that demonstrates the following tasks:

• Drawing graphics with predefined units.
• Centering graphics in the application's client area.
• Scaling graphics output to half its original size.
• Translating graphics output 3/4 of an inch to the right.
• Rotating graphics 30 degrees.
• Shearing graphics output along the x-axis.
• Reflecting graphics output about an imaginary horizontal axis drawn through its midpoint.

The following example was used to create the illustrations that appear earlier in this overview.

void TransformAndDraw(int iTransform, HWND hWnd)

{

HDC hDC;

XFORM xForm;

RECT rect;

 

// Retrieve a DC handle for the application's window.

 

hDC = GetDC(hWnd);

 

// Set the mapping mode to LOENGLISH. This moves the

// client area origin from the upper left corner of the

// window to the lower left corner (this also reorients

// the y-axis so that drawing operations occur in a true

// Cartesian space). It guarantees portability so that

// the object drawn retains its dimensions on any display.

 

SetGraphicsMode(hDC, GM_ADVANCED);

SetMapMode(hDC, MM_LOENGLISH);

 

// Set the appropriate world transformation (based on the

// user's menu selection).

 

switch (iTransform)

{

case SCALE: // Scale to 1/2 of the original size.

xForm.eM11 = (FLOAT) 0.5;

xForm.eM12 = (FLOAT) 0.0;

xForm.eM21 = (FLOAT) 0.0;

xForm.eM22 = (FLOAT) 0.5;

xForm.eDx = (FLOAT) 0.0;

xForm.eDy = (FLOAT) 0.0;

SetWorldTransform(hDC, &xForm);

break;

 

case TRANSLATE: // Translate right by 3/4 inch.

xForm.eM11 = (FLOAT) 1.0;

xForm.eM12 = (FLOAT) 0.0;

xForm.eM21 = (FLOAT) 0.0;

xForm.eM22 = (FLOAT) 1.0;

xForm.eDx = (FLOAT) 75.0;

xForm.eDy = (FLOAT) 0.0;

SetWorldTransform(hDC, &xForm);

break;

 

case ROTATE: // Rotate 30 degrees counterclockwise.

xForm.eM11 = (FLOAT) 0.8660;

xForm.eM12 = (FLOAT) 0.5000;

xForm.eM21 = (FLOAT) -0.5000;

xForm.eM22 = (FLOAT) 0.8660;

xForm.eDx = (FLOAT) 0.0;

xForm.eDy = (FLOAT) 0.0;

SetWorldTransform(hDC, &xForm);

break;

 

case SHEAR: // Shear along the x-axis with a

// proportionality constant of 1.0.

xForm.eM11 = (FLOAT) 1.0;

xForm.eM12 = (FLOAT) 1.0;

xForm.eM21 = (FLOAT) 0.0;

xForm.eM22 = (FLOAT) 1.0;

xForm.eDx = (FLOAT) 0.0;

xForm.eDy = (FLOAT) 0.0;

SetWorldTransform(hDC, &xForm);

break;

 

case REFLECT: // Reflect about a horizontal axis.

xForm.eM11 = (FLOAT) 1.0;

xForm.eM12 = (FLOAT) 0.0;

xForm.eM21 = (FLOAT) 0.0;

xForm.eM22 = (FLOAT) -1.0;

xForm.eDx = (FLOAT) 0.0;

xForm.eDy = (FLOAT) 0.0;

SetWorldTransform(hDC, &xForm);

break;

 

case NORMAL: // Set the unity transformation.

xForm.eM11 = (FLOAT) 1.0;

xForm.eM12 = (FLOAT) 0.0;

xForm.eM21 = (FLOAT) 0.0;

xForm.eM22 = (FLOAT) 1.0;

xForm.eDx = (FLOAT) 0.0;

xForm.eDy = (FLOAT) 0.0;

SetWorldTransform(hDC, &xForm);

break;

 

}

 

// Find the midpoint of the client area.

 

GetClientRect(hWnd, (LPRECT) &rect);

DPtoLP(hDC, (LPPOINT) &rect, 2);

 

// Select a hollow brush.

 

SelectObject(hDC, GetStockObject(HOLLOW_BRUSH));

 

// Draw the exterior circle.

 

Ellipse(hDC, (rect.right / 2 - 100), (rect.bottom / 2 + 100),

(rect.right / 2 + 100), (rect.bottom / 2 - 100));

 

// Draw the interior circle.

 

Ellipse(hDC, (rect.right / 2 -94), (rect.bottom / 2 + 94),

(rect.right / 2 + 94), (rect.bottom / 2 - 94));

 

// Draw the key.

 

Rectangle(hDC, (rect.right / 2 - 13), (rect.bottom / 2 + 113),

(rect.right / 2 + 13), (rect.bottom / 2 + 50));

Rectangle(hDC, (rect.right / 2 - 13), (rect.bottom / 2 + 96),

(rect.right / 2 + 13), (rect.bottom / 2 + 50));

 

// Draw the horizontal lines.

 

MoveToEx(hDC, (rect.right/2 - 150), (rect.bottom / 2 + 0), NULL);

LineTo(hDC, (rect.right / 2 - 16), (rect.bottom / 2 + 0));

 

MoveToEx(hDC, (rect.right / 2 - 13), (rect.bottom / 2 + 0), NULL);

LineTo(hDC, (rect.right / 2 + 13), (rect.bottom / 2 + 0));

 

MoveToEx(hDC, (rect.right / 2 + 16), (rect.bottom / 2 + 0), NULL);

LineTo(hDC, (rect.right / 2 + 150), (rect.bottom / 2 + 0));

 

// Draw the vertical lines.

 

MoveToEx(hDC, (rect.right/2 + 0), (rect.bottom / 2 - 150), NULL);

LineTo(hDC, (rect.right / 2 + 0), (rect.bottom / 2 - 16));

 

MoveToEx(hDC, (rect.right / 2 + 0), (rect.bottom / 2 - 13), NULL);

LineTo(hDC, (rect.right / 2 + 0), (rect.bottom / 2 + 13));

 

MoveToEx(hDC, (rect.right / 2 + 0), (rect.bottom / 2 + 16), NULL);

LineTo(hDC, (rect.right / 2 + 0), (rect.bottom / 2 + 150));

 

ReleaseDC(hWnd, hDC);

}