计算机图形学实验：二维图形变换

1、实验三二维图形变换一、实验任务1. 通过二维几何变换的数学模型,编写缩放、旋转、对称变换;2. 实现图形变换的交互式操作:缩放、旋转、对称变换等;二、实验内容1. 放大缩小变换放大缩小变换公式为:x =x.S x , y =y.S y ; 其中S x ,S y 分别为x,y 方向的放缩比例系数。变换矩阵表达式为:x y (1S x =S y =1.5;等比例放大(2S x =S y =0.5;等比例缩小2. 对称变换包括以x 轴对称、y 轴对称和原点O 对称三种。由于屏幕坐标只有第一象限,我们可以将原点平移到(500,240处。在第一象限画出一个三角形,然后分别求出三个对称图形。3. 旋转变换

2、将图形上的点(x ,y 旋转角度,得到新的坐标(x ,y 为:x =xcos -ysin , y =xsin +ycos ; x y 4.三、设计思路1. 通过二维几何变换的数学模型,编写缩放、旋转、对称变换;2. 以(500,240为原点建立图形变换的参考坐标系;3. 通过键盘按键控制图形的缩放、旋转、对称变换;4. 变换图形设定为以Pt0(540,220、Pt1(670,130、Pt2(560,120为顶点的三角形。步骤:1.建立Trans工程文件;2.利用Resource View设计菜单,如图所示; 3.在CTransView视图类中添加消息映射函数; 4.添加自定义的成员变量:CPo

3、int Pt3;/三角形定点数组float dAngle;/每一次旋转的角度在视图类CPP文件的构造函数中初始化成员变量Pt0.x = 540; Pt0.y = 220;Pt1.x = 670; Pt1.y = 130;Pt2.x = 560; Pt2.y = 120;dAngle = 0;5.在视图类的OnDraw(函数中加入下列代码,实现视图绘图。void CTransView:OnDraw(CDC* pDCCTransDoc* pDoc = GetDocument(;ASSERT_VALID(pDoc;/ TODO: add draw code for native data here/

4、绘出以以(540,220、(670,130、(560,120为顶点的三角形。pDC->MoveTo(Pt0;pDC->LineTo(Pt1;pDC->LineTo(Pt2;pDC->LineTo(Pt0;/绘出以(500,240为原点的坐标轴pDC->MoveTo(100,240;pDC->LineTo(900,240;pDC->MoveTo(500,5;pDC->LineTo(500,400;pDC->TextOut(900,235,"x轴"pDC->TextOut(500,400,"y轴"/

5、控制信息pDC->TextOut(15,10,"对称变换:键盘方向键"pDC->TextOut(15,28,"缩放变换:Z键缩小;X键放大"pDC->TextOut(15,46,"旋转变换:键盘R键"6.添加预编译常量#define PI 3.14159267.分别编写步骤3中向视图类中添加消息映射函数,程序如下:void CTransView:OnTransformRotate(/ TODO: Add your command handler code herefloat dRadiusAngle = 30.0 *

6、 PI /180.0;for(int i=0; i<3; i+Pti.x = Pti.x * cos(dRadiusAngle - Pti.y * sin(dRadiusAngle;Pti.y = Pti.x * sin(dRadiusAngle + Pti.y * cos(dRadiusAngle;RedrawWindow(;/实现图形旋转void CTransView:OnTransformScale(/ TODO: Add your command handler code herefloat dScaleX = 2.0;float dScaleY = 0.5;for(int i=

7、0; i<3; i+Pti.x *= dScaleX;Pti.y *= dScaleY;RedrawWindow(;/实现图形缩放void CTransView:OnTransformSymmetry(/ TODO: Add your command handler code herefor(int i=0; i<3; i+Pti.x += Pti.x;Pti.y += Pti.y;RedrawWindow(;/实现图形对称8.添加成员函数实现键盘交互式控制图形变换函数及代码如下:void CTransView:OnKeyDown(UINT nChar, UINT nRepCnt,

8、 UINT nFlags/ TODO: Add your message handler code here and/or call default int i=0;CPoint TmpPt = Pt0;switch (nCharcase VK_UP: /上for(i=0; i<3; i+Pti.y =240-(Pti.y-240;break;case VK_DOWN: /下for(i=0; i<3; i+Pti.y =240-(Pti.y-240;break;case VK_LEFT: /左for(i=0; i<3; i+Pti.x =500-(Pti.x-500;brea

9、k;case VK_RIGHT: /右for(i=0; i<3; i+Pti.x =500-(Pti.x-500;break;case 0X5A: /Z的ASCII码Pt1 = Pt1 - Pt0;Pt2 = Pt2 - Pt0;Pt0.x = Pt0.y = 0;for(i=1; i<3; i+Pti.x *= 0.5;Pti.y *= 0.5;Pt0 = TmpPt;Pt1 = Pt1 + Pt0;Pt2 = Pt2 + Pt0;break;case 0X58: /X的ASCII码Pt1 = Pt1 - Pt0;Pt2 = Pt2 - Pt0;Pt0.x = Pt0.y = 0

10、;for(i=1; i<3; i+Pti.x *= 2.0;Pti.y *= 2.0;Pt0 = TmpPt;Pt1 = Pt1 + Pt0;Pt2 = Pt2 + Pt0;break;case 0X52 : /R的ASCII码dAngle = -1.0;/每一次逆时针旋转一度float dRadiusAngle = dAngle * PI /180.0;Pt1 = Pt1 - Pt0;Pt2 = Pt2 - Pt0;Pt0.x = Pt0.y = 0;for(int i=1; i<3; i+ /由于CPoint的x和y坐标值都为正值,所以如果计算出是负值来时,就直接赋0Pti.x = (floatPti.x * cos(dRadiusAngle - (floatPti.y * sin(dRadiusAngle;Pti.y = (floatPti.x * sin(dRadiusAngle + (floatPti.y * cos(dRadiusAngle;Pt0 = TmpPt;Pt1 = Pt1 + Pt0; Pt2 = Pt2 + P