4、三角函数
我们知道,三角函数主要有这样几个公式:
sin(a) = 对边a /
斜边c
cos(a) = 底边b / 斜边c (其中角度a,可以是任意角度)
如下图所示:
由图可知,在一周之内,角度a可以在从0度到360度取值而对于钟表来说,每个刻度之间的度数差别为360度除以60个刻度,等于6度,也就是说公式里的角度a已经知道了.而且可知边a实际上就是圆上任意一点在y轴上的坐标,而边b是加上就是圆上任意一点在x轴上的坐标,半径r由我们所要画出的圆形的大小决定的,所以我们可以得到圆上任意一点在坐标系中的x
, y轴上的取值.公式如下:
x = sin(a) * r
y = cos(a) *
r
而且在vb中,也有这样的函数可供使用.
1、cos函数
作用：返回一个Double，指定一个角度的余弦值
格式：
Cos(number)
2、sin函数
作用：返回一个Double，指定一个角度的正弦值
格式：
Sin(number)
下面我们通过示例来看看具体的用法。
首先，我们将用这些知识来画出一个正弦：
下面是代码：
'=======================
'说明,x从0到form1的最右面
'y值中,因为i是从0变到form1的最右面
'所以i/form1.scalewidth
就从0 变到1
'所以,i/form1.scalewidth*2*3.1415926既是o*2pi 到1*
2pi
'所以,cos(i/form1.scalewidth*2*3.1415926),就从1到-1,在变到1
'所以,1-cos(i/form1.scalewidth*2*3.1415926),就从0到2,在变到0
'所以y
就从0到form1.scaleheight,在变到0
'即可画出cos曲线
'=======================
Private
Sub huacos ( ) ‘自定义了一个名为huacos的过程
Dim x As Double
Dim y As
Double
For i = 0 To Form1.ScaleWidth ‘设定周期为Form1 .
ScaleWidth
x = i
y = (1–Cos(i/ Form1.ScaleWidth * 2 * 3.1415926
) ) * Form1.ScaleHeight/2
‘
因为三角函数中的角度的增长方向,和计算机中相反,所以要用1减去cos值
PSet(x,y)
Next i
End
Sub
Private Sub Form _ Activate ( )
Huacos ‘调用huacos 过程
End
Sub |
下图为运行结果：
余弦和它相似，代码如下：
Private Sub huasin ( ) ‘自定义了一个名为huasin的过程
Dim x As
Double
Dim y As Double
For i = 0 To Form1 . ScaleWidth
‘设定周期为Form1 . ScaleWidth
x = i
y =
(1–Sin(i/Form1.ScaleWidth*2*3.1415926)) * Form1.ScaleHeight / 2
‘
因为三角函数中的角度的增长方向,和计算机中相反,所以要用1减去sin值
PSet (x, y)
Next i
End
Sub
Private Sub Form _ Activate ( )
huasin ‘调用huasin过程
End
Sub |
下图为运行结果：
有了这些基础,画出一个正圆也就没问题了。请看下面的代码。
Private Sub huayuan( )
Dim x As Double
Dim y As
Double
For i = 0 To
360
x=(1–Sin(i/360*2*3.1415926))*(Form1.ScaleHeight/2–100)+100
y=(1–Cos(i/360*2*3.1415926))*(Form1.ScaleHeight/2–100)+100
Pset(x,y)
Next
i
End Sub
Private Sub Form _ Activate( )
huayuan
End
Sub |
上面的代码不难,好好思考一下吧.下面是运行结果：
上面的例子里，我们使用360个点组成了一个密集度挺高的圆形，可是既然vb中已给我们提供了现成的画圆形的函数，为什么不用呢？但通过上面的例子，我们应该想到，如果我们将360个点，变成60个点，那不就正好是一个钟表的刻度吗？！这样的话我们只需要改动两个地方，一个是点的个数，另一个是点与点之间的弧度，应该为360度的60分之一，也就是每60度画一个点。代码如下：
Private Sub huabiaopan ( )
Dim x As Double
Dim y As
Double
For i = 0 To 60
x=( 1 –
Sin(i/60*2*3.1415926))*(Form1.ScaleHeight/2–100)+100
y=( 1 –
Cos(i/60*2*3.1415926))*(Form1.ScaleHeight/2–100)+100
PSet(x,y)
Next
i
End Sub
Private Sub Form _ Activate (
)
huabiaopan
End Sub |
下面是运行结果：
(为了看得清楚些,我将颜色设为了红色,大家可以随喜好自行修改,方法当然是在Pset函数中了)
看来我们距离成功越来越近了。对于钟表里的三个针来说，每一时刻都会指向其中一个刻度，所以我们只要在其中添加代码，让它实现从圆心到所指刻度画直线就可以实现钟表里的三个针了。
下面是关于其中一个针的走动，代码如下：
Private Function huamiao ( a As Integer
)
'用同背景相同的颜色，在前一次的位置上，从新画直线，抹除前一次画的线
x
=(1–Sin((a+1)/60*2*3.1415926))*(Form1.ScaleHeight/2–200)+200
y
=(1–Cos((a+1)/60*2*3.1415926))*(Form1.ScaleHeight/2–200)+200
Line(Form1.ScaleHeight/2,Form1.ScaleHeight/2)-(x,y),QBColor
( 7 )
'然后开始画後一秒的线
x =(1–Sin(a/60 * 2 * 3.1415926 ) ) *
(Form1.ScaleHeight/2–200)+200
y =(1–Cos(a/60 * 2 * 3.1415926 ) ) *
(Form1.ScaleHeight/2–200)+200
Line(Form1.ScaleHeight/2,Form1.ScaleHeight/2)-(x,y),QBColor
( 1 )
huamiao = a - 1
End Function
Private Sub
Timer1 _ Timer ( )
mz =Second(time)
mz =60–mz
‘因为三角函数中，角度的变化方向，正好与钟表的方向相反，
‘所以60减去就相当于将角度变为负值，也就是说，和原来的角度增长方向正好相反，与钟表的增长方向相同。
mz
= huamiao ( mz )
End Sub |
下面是运行效果：
好了,现在我们可以加上,分针和时针了.下面是源代码和运行结果:
' = = = = = = = = = = = = = = = = = = = = = =
' 以下语句能画出表盘
‘
六十个点表示六十个刻度,
' = = = = = = = = = = = = = = = = = = = = =
=
Private Sub huayuan ( )
Dim x As Double
Dim y As
Double
For i = 0 To 60
x = ( 1 – Sin ( i / 60 * 2 * 3.1415926
) ) * ( Form1.ScaleHeight / 2 – 100 ) + 100
y = ( 1 – Cos ( i / 60 *
2 * 3.1415926 ) ) * ( Form1.ScaleHeight / 2 – 100 ) + 100
PSet ( x ,
y ) , QBColor ( 12 )
Next i
End Sub
‘ = = = = = = = = = = =
= = = = = = = = = = = = = =
=
‘下面代码作用是画出时针走的路线
‘时针是12个刻度,表示是12个钟点
‘ = = = = = = =
= = = = = = = = = = = = = = = = = = =
Private Function xianshishi (
a As Integer )
'抹除前一次画的线
x = (1–Sin((a+1)/12*2*3.1415926))
* ( Form1.ScaleHeight/2–800)+800
y = (1–Cos((a+1)/12*2*3.1415926)) * (
Form1.ScaleHeight/2–800)+800
Line
(Form1.ScaleHeight/2,Form1.ScaleHeight/2)-(x,y),QBColor(7)
'开始画後一秒的线
x
= (1–Sin(a/12*2*3.1415926))*(Form1.ScaleHeight/2–800)+800
y =
(1–Cos(a/12*2*3.1415926))*(Form1.ScaleHeight/2–800)+800
Line
(Form1.ScaleHeight/2,Form1.ScaleHeight/2)-(x,y),QBColor ( 1
)
xianshishi=a-1
End Function
‘ = = = = = = = = = = = = = =
= = = = = = = = = = =
=
‘下面代码作用是画出秒针走的路线
‘秒针是六十个刻度,表示是六十个秒点
‘ = = = = = = =
= = = = = = = = = = = = = = = = = = =
Private Function xianshimiao
( a As Integer )
'抹除前一次画的线
x
=(1–Sin((a+1)/59*2*3.1415926))*(Form1.ScaleHeight/2–200)+200
y
=(1–Cos((a+1)/60*2*3.1415926))*(Form1.ScaleHeight/2–200)+200
Line(Form1.ScaleHeight/2,Form1.ScaleHeight/2)-(x,y),QBColor(7)
'开始画後一秒的线
x
= (1–Sin(a/59*2*3.1415926))*(Form1.ScaleHeight/2–200)+200
y =
(1–Cos(a/60*2*3.1415926))*(Form1.ScaleHeight/2–200)+200
Line (
Form1.ScaleHeight/2 ,Form1.ScaleHeight/2)-(x,y),QBColor(1)
xianshimiao
= a - 1
End Function
‘ = = = = = = = = = = = = = = = = = = = =
= = = = = =
‘下面代码作用是画出分针走的路线
‘分针是六十个刻度,表示是六十个分点
‘
= = = = = = = = = = = = = = = = = = = = = = = = = =
Private
Function xianshifen ( a As Integer )
'抹除前一次画的线
x
=(1–Sin((a+1)/59 * 2 * 3.1415926)) * ( Form1.ScaleHeight/2–400)+400
y
=(1–Cos((a+1)/60 * 2 * 3.1415926)) * (
Form1.ScaleHeight/2–400)+400
Line
(Form1.ScaleHeight/2,Form1.ScaleHeight/2)-(x,y),QBColor(7)
'开始画後一秒的线
x
=(1–Sin(a/59*2*3.1415926)) * (Form1.ScaleHeight/2–400) + 400
y
=(1–Cos(a/60*2*3.1415926)) * (Form1.ScaleHeight/2–400) + 400
Line
(Form1.ScaleHeight/2,
Form1.ScaleHeight/2)-(x,y),QBColor(1)
xianshifen = a -
1
End Function
‘ = = = = = = = = = = = = = = = = = = = = = =
= =
‘ 每秒钟触发一次此事件,从而获取当时的时间,并调用相应的函数,画出三个针的位置
‘ = = = = = = =
= = = = = = = = = = = = = = = = =
Private Sub Timer1 _ Timer (
)
miao = Second (time)
miao = 60 – miao
fen = Minute
(time)
fen = 60 - fen
shi = Hour (time)
If shi > = 12
Then ‘因为一天之内时针要走二十四个钟头,也就是要走两圈,所以将下午和晚上的时间减去十二,就可以确定时针准确的位置
shi =
shi - 12
End If
shi = 12 - shi
miao = xianshimiao (
miao )
fen = xianshifen ( fen )
shi = xianshishi ( shi
)
End Sub
‘ = = = = = = = = = = = = = = =
=
‘此事件,在窗体最初载入时触发,主要作用是画出表盘和刻度
‘ = = = = = = = = = = = = = =
= =
Private Sub Form _ Load ( )
Form1.Width =
Form1.Height-250
Huayuan
‘画刻度
Form1.Circle(Form1.ScaleHeight/2,Form1.ScaleHeight/2),Form1.ScaleHeight/2-30
End
Sub |
运行效果如下图所示:
|
