在picture上画了一个直线和一个三角形，如何让它顺时针旋转30度重画？

原点旋转：
X'=x*cos(th)-y*sin(th)
Y'=y*sin(th)+x*cos(th)绕基准点旋转需要：平移、旋转、再平移回去

x1 = x * Cos(α) + y * Sin(α)
y1 = -x * Sin(α) + y * Cos(α)x1 和 Y1是新的坐标，α是旋转的弧度，这个公式是绕坐标原点进行旋转，如果要绕某一确定的点，要将坐标相对该点进行坐标变换

不小心写错了
X'=x*cos(th)-y*sin(th)
Y'=x*sin(th)+y*cos(th)

给你一个我以前为一个帖子写的三维点旋转的例子吧。窗体中放置line控件数组，命名为line1,下标从0~11，然后粘铁下面的代码Option Explicit
Const Lenth = 1000
Const StartPoint = 2000
Private Type Point_3D
    x As Double
    y As Double
    z As Double
End Type
Dim P_3D(7) As Point_3DPrivate Sub Form_Load()
    P_3D(0).x = Lenth
    P_3D(0).y = Lenth
    P_3D(0).z = Lenth

    P_3D(1).x = Lenth
    P_3D(1).y = -Lenth
    P_3D(1).z = Lenth

    P_3D(2).x = -Lenth
    P_3D(2).y = Lenth
    P_3D(2).z = Lenth

    P_3D(3).x = -Lenth
    P_3D(3).y = -Lenth
    P_3D(3).z = Lenth

    P_3D(4).x = Lenth
    P_3D(4).y = Lenth
    P_3D(4).z = -Lenth

    P_3D(5).x = Lenth
    P_3D(5).y = -Lenth
    P_3D(5).z = -Lenth

    P_3D(6).x = -Lenth
    P_3D(6).y = Lenth
    P_3D(6).z = -Lenth

    P_3D(7).x = -Lenth
    P_3D(7).y = -Lenth
    P_3D(7).z = -Lenth
    Call Draw_3D
End Sub
Private Sub Draw_3D()
    Line1(0).X1 = P_3D(0).x + StartPoint
    Line1(0).Y1 = P_3D(0).y + StartPoint
    Line1(0).X2 = P_3D(1).x + StartPoint
    Line1(0).Y2 = P_3D(1).y + StartPoint    Line1(1).X1 = P_3D(0).x + StartPoint
    Line1(1).Y1 = P_3D(0).y + StartPoint
    Line1(1).X2 = P_3D(2).x + StartPoint
    Line1(1).Y2 = P_3D(2).y + StartPoint    Line1(2).X1 = P_3D(2).x + StartPoint
    Line1(2).Y1 = P_3D(2).y + StartPoint
    Line1(2).X2 = P_3D(3).x + StartPoint
    Line1(2).Y2 = P_3D(3).y + StartPoint    Line1(3).X1 = P_3D(3).x + StartPoint
    Line1(3).Y1 = P_3D(3).y + StartPoint
    Line1(3).X2 = P_3D(1).x + StartPoint
    Line1(3).Y2 = P_3D(1).y + StartPoint    Line1(4).X1 = P_3D(4).x + StartPoint
    Line1(4).Y1 = P_3D(4).y + StartPoint
    Line1(4).X2 = P_3D(5).x + StartPoint
    Line1(4).Y2 = P_3D(5).y + StartPoint    Line1(5).X1 = P_3D(5).x + StartPoint
    Line1(5).Y1 = P_3D(5).y + StartPoint
    Line1(5).X2 = P_3D(7).x + StartPoint
    Line1(5).Y2 = P_3D(7).y + StartPoint    Line1(6).X1 = P_3D(6).x + StartPoint
    Line1(6).Y1 = P_3D(6).y + StartPoint
    Line1(6).X2 = P_3D(7).x + StartPoint
    Line1(6).Y2 = P_3D(7).y + StartPoint    Line1(7).X1 = P_3D(4).x + StartPoint
    Line1(7).Y1 = P_3D(4).y + StartPoint
    Line1(7).X2 = P_3D(6).x + StartPoint
    Line1(7).Y2 = P_3D(6).y + StartPoint    Line1(8).X1 = P_3D(2).x + StartPoint
    Line1(8).Y1 = P_3D(2).y + StartPoint
    Line1(8).X2 = P_3D(6).x + StartPoint
    Line1(8).Y2 = P_3D(6).y + StartPoint    Line1(9).X1 = P_3D(0).x + StartPoint
    Line1(9).Y1 = P_3D(0).y + StartPoint
    Line1(9).X2 = P_3D(4).x + StartPoint
    Line1(9).Y2 = P_3D(4).y + StartPoint    Line1(10).X1 = P_3D(5).x + StartPoint
    Line1(10).Y1 = P_3D(5).y + StartPoint
    Line1(10).X2 = P_3D(1).x + StartPoint
    Line1(10).Y2 = P_3D(1).y + StartPoint    Line1(11).X1 = P_3D(3).x + StartPoint
    Line1(11).Y1 = P_3D(3).y + StartPoint
    Line1(11).X2 = P_3D(7).x + StartPoint
    Line1(11).Y2 = P_3D(7).y + StartPoint

End Sub
Private Sub Form_KeyDown(KeyCode As Integer, Shift As Integer)
    Dim j As Double

    Select Case KeyCode
        Case 39 '右
            j = 1 / 180 * 3.1415926
            rote_y j
        Case 37 '左
            j = -1 / 180 * 3.1415926
            rote_y j
        Case 40 '下
            j = -1 / 180 * 3.1415926
            rote_x j
        Case 38 '上
            j = 1 / 180 * 3.1415926
            rote_x j
    End Select
    Draw_3D
End Sub
Private Sub rote_y(j As Double)
'x=x*cosa+z*sina,y=y,z=-x*sina+z*cosa
    Dim i As Integer
    For i = 0 To 7
        P_3D(i).x = P_3D(i).x * Cos(j) + P_3D(i).z * Sin(j)
        P_3D(i).z = -P_3D(i).x * Sin(j) + P_3D(i).z * Cos(j)
    NextEnd Sub
Private Sub rote_x(j As Double)
'x=x,y=y*cosa-z*sina,z=y*sina+z*cosa
    Dim i As Integer
    For i = 0 To 7
        P_3D(i).y = P_3D(i).y * Cos(j) - P_3D(i).z * Sin(j)
        P_3D(i).z = P_3D(i).y * Sin(j) + P_3D(i).z * Cos(j)
    Next
End Sub

To chewinggum(口香糖·dotnet转型中) ：
你这个公式我怎么越看越像(3D)Y轴旋转公式
只不过将Z替换成Y了

2D的都是以Z轴位旋转轴，旋转XY坐标

画的图形是2d的，按照上面的公式好像短很多啊。Private Sub Command1_Click()
Picture1.Line (20, 45)-(50, 45)
End SubPrivate Sub Command2_Click()
Dim a, b, c, d As Single
a = Math.Abs(50 * Math.Cos(120) - 45 * Math.Sin(120))
b = Math.Abs(50 * Math.Sin(120) + 45 * Math.Cos(120))
c = Math.Abs(20 * Math.Cos(120) - 45 * Math.Sin(120))
d = Math.Abs(20 * Math.Sin(120) + 45 * Math.Cos(120))Picture1.Line (c, d)-(a, b)End Sub这个是旋转120度

to zyl910(910：分儿，我又来了！)
我的那段代码前面的说明补救已经说是3D的旋转了吗，这段代码是从2D旋转改过来的，只是为了让楼主龛格例子而已，理解了在改回2D根本就是非常简单的问题，只不过我懒得改回去而已

OK 现在再来一段二维的旋转，窗体内直接拷贝下面的代码，按左右方向键旋转三角形Option Explicit
Private Type Point_2D
    x As Double
    y As Double
End Type
Dim RoteCenter As Point_2D '旋转中心
Dim P_2D(2) As Point_2DPrivate Sub Form_Load()
    Me.AutoRedraw = True
    'Me.Cls

    P_2D(0).x = 1000
    P_2D(0).y = 1000

    P_2D(1).x = 2000
    P_2D(1).y = 2500

    P_2D(2).x = 2000
    P_2D(2).y = 1000

    RoteCenter.x = P_2D(1).x '设定旋转中心为P_2D(1)
    RoteCenter.y = P_2D(1).y
    Call draw
End SubPrivate Sub draw()
    Dim i As Integer
    Me.CurrentX = P_2D(0).x
    Me.CurrentY = P_2D(0).y

    For i = 0 To 2
        Me.Line -(P_2D(i).x, P_2D(i).y)
    Next

    Me.Line -(P_2D(0).x, P_2D(0).y)
End SubPrivate Sub Form_KeyDown(KeyCode As Integer, Shift As Integer)
    Dim j As Double

    Select Case KeyCode
        Case 39 '右
            j = 1 / 180 * 3.1415926
            rote j
        Case 37 '左
            j = -1 / 180 * 3.1415926
            rote j
    End Select
    Me.Cls
    Call draw
End SubPrivate Sub rote(j As Double)
'x=x*cosa+z*sina,y=y,z=-x*sina+z*cosa
    Dim i As Integer
    For i = 0 To 2
        P_2D(i).x = P_2D(i).x - RoteCenter.x * Cos(j) + (P_2D(i).y - RoteCenter.y) * Sin(j) + RoteCenter.x
        P_2D(i).y = -(P_2D(i).x - RoteCenter.x) * Sin(j) + (P_2D(i).y - RoteCenter.y) * Cos(j) + RoteCenter.y
    NextEnd Sub

我来回答这个问题：
1、选定旋转中心点(XCen，YCen)；
2、旋转点相对于中心点的自然数学坐标（X从左向右为正向，与屏幕坐标方向一致；Y从下向上为正向，与屏幕坐标相反。）；
   XNew=XOld-XCen
   YNew=-(YOld-YCen)
3、旋转公式推导：
   旋转前所处位置
   ZNew=re^(ja)，j=√-1   XNew=rCos(a)
   YNew=rSin(a)
   旋转
   ZRot=re^(j(a+b))，j=√-1，b—旋转角(弧度)，逆时针为正。   XRot=rCos(a+b)=r(Cos(a)Cos(b)-Sin(a)Sin(b))=XNew*Cos(b)-YNew*Sin(b)
   YRot=rSin(a+b)=r(Sin(a)Cos(b)+Cos(a)Sin(b))=YNew*Cos(b)+XNew*Sin(b)
   XResult=XCen+XRot
   YResult=YCen-YRot

调试易

在picture上画了一个直线和一个三角形，如何让它顺时针旋转30度重画？

解决方案 »