踢馆帝
踢馆帝原创小测试，第五题！
本帖最后由 踢馆帝 于 2012-6-23 16:12 编辑
由于搬砖很辛苦，很久没出题了，终于放假了，先出一个吧
三维空间中有两个球，球心坐标分别是L1，L2。 ，半径是R1，R2。
现在两个球分别以速度V1，V2开始做直线运动（V1，V2也是三个分量的向量）
写一个小程序，给定（输入）L1，L2，R1，R2，V1，V2
基础题：判断两个球是否相撞。
扩展题：附加给定两个球的质量M1，M2。
如果相撞，求出相撞后两个球的速度V3，V4。
（假设这个空间没有任何阻力，摩擦，并且球碰撞是弹性碰撞，也就是碰撞不损失能量）
这里给出一组简单的数据，可供测试：(基础题)
L1 = (10,0,0)
L2 = (0,10,0)
V1 = (-1,0,0)
V2 = (0,-1,0)
得出的碰撞时刻是10-sqrt(2)
踢馆帝
大家积极性不高哇
展开Biu
大家积极性不高哇，先给出解答吧
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轻舟过
附加题只要求碰撞时刻两球心连线方向的动量守
展开Biu
想了下，附加题只要求碰撞时刻两球心连线方向的动量守恒和能量守恒就行
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踢馆帝
面瘫大明神
展开Biu
面瘫大明神 发表于 2012-6-24 17:23 
这是数学问题吧
是什么问题不重要，重要的是解决问题
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面瘫大明神
这是数学问题吧
展开Biu
@@16!!这是数学问题吧
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LonghronShen
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展开Biu
本帖最后由 LonghronShen 于 2012-6-22 22:41 编辑
都占坑了啊，那我也来一个
先做出基础题。
算法：
ImportsMicrosoft.Xna.Framework
ImportsSystem.Runtime.CompilerServices
 
ModuleModuleMain
 
    Public Class Ball
 
        Public Property Center() As Vector3
        Public Property R() As Double
        Public Property Mass() As Double
 
        Public ReadOnly Property IsLegal() As Boolean
            Get
                With Me.Center
                    Dim parts = {.X,.Y, .Z}
                    For Each p In parts
                        If Single.IsInfinity(p)Or Single.IsNaN(p)Then
                            Return False
                        End If
                    Next
                End With
                Return Me.R <>0
            End Get
        End Property
 
        Public Sub New()
            Me.Center =Vector3.Zero
            Me.R = 0
        End Sub
 
        Public Sub New(ByVal p As Vector3, ByVal r As Double, ByVal m As Double)
            Me.Center = p
            Me.R = r
            Me.Mass = m
        End Sub
 
        Public Sub New(ByVal p As Vector4)
            Me.Center = New Vector3(p.X,p.Y, p.Z)
            Me.R = p.W
        End Sub
 
        Public Sub New(ByVal ParamArray p() As Double)
            If p.Length >= 4 Then
                Me.Center = New Vector3(p(0), p(1), p(2))
                Me.R = p(3)
                If p.Length >=5 Then
                    Me.Mass =p(4)
                End If
            Else
                Throw New ArgumentException("Too few arguments for Ball contructor.")
            End If
        End Sub
 
    End Class
 
    Public Function CreateVector4FromString(ByVal s As String, ByVal ParamArray sp() As String) As Vector4
        Dim parts = s.Split(sp,StringSplitOptions.RemoveEmptyEntries)
        If parts.Length >= 4 Then
            Return New Vector4(parts(0), parts(1), parts(2), parts(3))
        Else
            Throw New ArgumentException("Wrong format for Vector4.")
        End If
    End Function
 
    Public Function CreateVector3FromString(ByVal s As String, ByVal ParamArray sp() As String) As Vector3
        Dim parts = s.Split(sp,StringSplitOptions.RemoveEmptyEntries)
        If parts.Length >= 3 Then
            Return New Vector3(parts(0), parts(1), parts(2))
        Else
            Throw New ArgumentException("Wrong format for Vector3.")
        End If
    End Function
 
    Public Function Root(ByVal f As Func(Of Double, Double), ByVal f_ As Func(Of Double, Double), Optional ByVal x As Double = 0) As Double
        If f(x) = 0 Then Return x
        Dim stw As New Stopwatch()
        stw.Start()
        Dim x0 = x
        Do
            x0 = x
            Dim vf = f(x0)
            Dim vf_ = f_(x0)
            x = x - vf/ vf_
        Loop While Math.Abs((x - x0))>= 0.00001 Andstw.Elapsed.TotalSeconds < 20
        stw.Stop()
        If stw.Elapsed.TotalSeconds >20 Then
            Throw New ArgumentException("Timeout when finding the root.")
        End If
        Return x
    End Function
 
    Public Function GenericCast(Of U, V)(ByVal obj As U) As V
        Try
            Return CType(DirectCast(obj, Object), V)
        Catch ex As InvalidCastException
            Return DirectCast(CompilerServices.Conversions.ChangeType(obj,GetType(V)), V)
        End Try
    End Function
 
    <Extension()>_
    Public Function OfType(Of U, V)(ByVal [Me] As IEnumerable(OfU)) As IEnumerable(OfV)
        Dim lst As New List(Of V)
        For Each item In [Me]
            lst.Add(GenericCast(OfU, V)(item))
        Next
        Return lst
    End Function
 
    Public Sub Pause()
        Console.WriteLine("Press any key to continue.")
        Console.ReadKey(True)
    End Sub
 
    Sub Main()
        While True
            Try
                Console.WriteLine("Please input data for the first ball.")
                Console.WriteLine("x, y, z, r,[m]")
                Dim b1 = New Ball(Console.ReadLine().Split(",").OfType(Of Double)().ToArray())
                If b1.IsLegal =False Then
                    Throw New ArgumentException("The data for the first ball is illegal.")
                End If
 
                Console.WriteLine("Please input data for the second ball.")
                Console.WriteLine("x, y, z, r,[m]")
                Dim b2 = New Ball(Console.ReadLine().Split(",").OfType(Of Double)().ToArray())
                If b2.IsLegal =False Then
                    Throw New ArgumentException("The data forthe second ball is illegal.")
                End If
 
                Console.WriteLine("Please input the velocity for the first ball.")
                Console.WriteLine("Vector3: x, y,z")
                Dim v1 =CreateVector3FromString(Console.ReadLine(), ",")
 
                Console.WriteLine("Please input the velocity for the second ball.")
                Console.WriteLine("Vector3: x, y,z")
                Dim v2 = CreateVector3FromString(Console.ReadLine(),",")
 
                Dim dis =
                    Function(t As Double)
                        Return Vector3.Distance(
                            New Vector3(b1.Center.X+ v1.X * t,
                                       b1.Center.Y + v1.Y * t,
                                       b1.Center.Z + v1.Z * t),
                            New Vector3(b2.Center.X+ v2.X * t,
                                       b2.Center.Y + v2.Y * t,
                                       b2.Center.Z + v2.Z * t))
                    End Function
                Dim _dis =
                    Function(t As Double)
                        Dim g_ = Function(_t As Double)
                                    Return 2 * (Vector3.Distance(v1,v2) ^ 2) * _t +
                                       2 * ((b1.Center.X- b2.Center.X) * (v1.X - v2.X) +
                                             (b1.Center.Y- b2.Center.Y) * (v1.Y - v2.Y) +
                                             (b1.Center.Z- b2.Center.Z) * (v1.Z - v2.Z))
                                 End Function
                        Return 0.5 * Math.Pow(dis(t)^ 2, -0.5) * g_(t)
                    End Function
 
                Dim time = Root(dis,_dis)
                If dis(time)<= Math.Abs(b1.R + b2.R) Then
                    Dim oldColor =Console.ForegroundColor
                   Console.ForegroundColor = ConsoleColor.Red
                    Console.WriteLine("The two balls will collide with each other.")
                   Console.ForegroundColor = oldColor                    
                Else
                   Console.WriteLine("The two balls will not collide with eachother.")
                End If
 
                Call Pause()
            Catch ex As Exception
                Console.WriteLine(ex.Message& vbCrLf & ex.StackTrace.ToString())
                Call Pause()
                Console.Clear()
                Continue While
            End Try
        End While
    End Sub
 
End Module
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踢馆帝
话说赶紧做题
展开Biu
ぃ野花のAriosモ 发表于 2012-6-21 22:41 
好头像
好眼力
喂喂喂，话说赶紧做题
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秋声赋
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展开Biu
本帖最后由 秋声赋 于 2012-6-22 00:38 编辑
没仔细检查
先放在这
就说思路 代码也没仔细看
先求相对速度和距离
因为没时间，所以规范化向量
以相对速度做一个坐标轴（原点在一个球的球心）
这时 2个球在该平面（相对速度向量过新坐标系原点的正交补）的投影就是2个圆了
然后就是求这两个球心在这个平面上的距离
想想下很容易看出 相对速度，相对距离，投影平面圆心的距离是一个三角形
求出投影平面的圆心距离
然后就是2D的判断圆是否相交
[mw_shl_code=csharp,true]
bool IsPeng=false;
Vector3D L1 = new Vector3D(1, 1, 1);
Vector3D L2 = new Vector3D(1, 1, 1);
double R1 = 1;
double R2 = 1;
Vector3D V1 = new Vector3D(1, 1, 1);
Vector3D V2 = new Vector3D(1, 1, 1);
Vector3D RV = V2 - V1;
Vector3D RX = L2 - L1;
RV.Normalize();
RX.Normalize();
if ((RX - RV).Length > (RX + RV).Length) return;
double RC = Math.Sqrt(RX.LengthSquared - RV.LengthSquared);
if (RC > R1 + R2) IsPeng = false;
else IsPeng = true;
[/mw_shl_code]
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ぃ野花のAriosモ