前言

想必大家在使用 SolidWorks 时，尤其是想要截图的时候，因为视角的关系，竖直方向的边线通常会出现锯齿（1080p 及以下的屏幕尤为明显）。而如果手动通过鼠标改变视角到边线无锯齿又很困难，因此打算写一个能自动改变视角的宏程序。

Y向边线有锯齿
Y 向边线有锯齿
Y向边线无锯齿
Y 向边线无锯齿

原理

根据 SolidWorks 官方 api 文档 IMathTransform Interface - 2022 - SOLIDWORKS API Help 可知，控制视角的是一个 3x3 的单位矩阵（a~i）。再结合 Orientation3 这个函数，就有矩阵数组

abcn
defo
ghip
jklm
01213
34514
67815
9101112
  • 第 0-2 位：X 轴单位向量（坐标）。
  • 第 3-5 位：Y 轴单位向量（坐标）。
  • 第 6-7 位：Z 轴单位向量（坐标）。
  • 第 9-11 位：平移分量，本文不涉及。
  • 第 12 位：缩放因子，一般为 1 就行。
  • 第 13-15 位：保留，不使用。

可能有些人会很奇怪，坐标轴的向量不应该是固定的吗，为什么会变呢。这是因为旋转时，视角和绝对坐标系不是重合的，这里的 XYZ 坐标轴单位向量可以理解为两者之差。

主要算法逻辑：计算 XYZ 坐标轴向量各自与 YZ 平面的夹角，选出最合适的坐标轴（夹角最小的坐标轴），再算出旋转轴向量后，再按罗德里格公式计算出剩下的坐标轴向量。

实操

获取当前视角

这里注意，Orientation3 的返回值不是 Variant 而是 Object，所以需要用 ArrayData 方法获取 Variant。For 循环里的就是按 XYZ 打印的视角向量。

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Dim swApp As SldWorks.SldWorks
Dim swModel As SldWorks.ModelDoc2
Dim swModelView As SldWorks.ModelView
Dim Matrix As SldWorks.MathTransform

Set swApp = Application.SldWorks
Set swModel = swApp.ActiveDoc
Set swModelView = swModel.ActiveView
Set Matrix = swModelView.Orientation3

Debug.Print "Orignal Orientation Martrix: "
Dim i As Integer
For i = 0 To 9 Step 3
    Debug.Print Matrix.ArrayData(i), Matrix.ArrayData(i + 1), Matrix.ArrayData(i + 2)
Next i

向量点乘

因为 VBA 没有专门的向量点乘方法，所以需要自己写一个。关于什么是向量点乘请参阅几何向量的点乘 - 小时百科。

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Function Dot(m As Variant, n As Variant) As Variant
    Dot = Array(m(0) * n(0), m(1) * n(1), m(2) * n(2))
End Function

向量叉乘

因为 VBA 没有专门的向量叉乘方法，所以需要自己写一个。关于什么是向量叉乘请参阅几何向量的叉乘 - 小时百科。

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Function Cross(m As Variant, n As Variant) As Variant
    Cross = Array( _
        m(1) * n(2) - m(2) * n(1), _
        m(2) * n(0) - m(0) * n(2), _
        m(0) * n(1) - m(1) * n(0))
End Function

向量与平面夹角

此处计算的是向量 v 和 YZ 平面的夹角。参考【IB】线线角、线面角、面面角 - 知乎。

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Dim alpha As Double
alpha = Arcsin(Abs_v(Dot(v, Array(1, 0, 0))))

' 向量的模长
Function Abs_v(v As Variant) As Double
    Abs_v = Sqrt(v(0) ^ 2 + v(1) ^ 2 + v(2) ^ 2)
End Function

罗德里格旋转公式

这是三维空间中，一个向量绕旋转轴旋转给定角度以后得到的新向量的计算公式。这个公式使用原向量、旋转轴及它们叉积表示出旋转后的向量。详情可参阅罗德里格旋转公式、定轴旋转矩阵 - 小时百科。

罗德里格旋转公式图示
罗德里格旋转公式图示

$$ \boldsymbol{\mathbf{r}} ‘ = \boldsymbol{\mathbf{r}} \cos\theta + \overrightarrow{\boldsymbol{\mathbf{A}}} \boldsymbol\times \boldsymbol{\mathbf{r}} \sin\theta + \overrightarrow{\boldsymbol{\mathbf{A}}} ( \overrightarrow{\boldsymbol{\mathbf{A}}} \boldsymbol\cdot \boldsymbol{\mathbf{r}} ) (1 - \cos\theta)~ $$

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'm原向量；n旋转轴向量；a旋转角度
Function Rodrigues(m As Variant, n As Variant, a As Double) As Variant
    Rodrigues = Array( _
        m(0) * Cos(a) + Sin(a) * Cross(n, m)(0) + (1 - Cos(a)) * Dot(n, Dot(n, m))(0), _
        m(1) * Cos(a) + Sin(a) * Cross(n, m)(1) + (1 - Cos(a)) * Dot(n, Dot(n, m))(1), _
        m(2) * Cos(a) + Sin(a) * Cross(n, m)(2) + (1 - Cos(a)) * Dot(n, Dot(n, m))(2))
End Function

小试牛刀

这里假定 Y 轴向量的夹角最小，先算出 Y 轴向量旋转到 YZ 平面的坐标，再算出对应的旋转轴向量，以此最后算出 X 和 Z 轴向量。其他轴的情况同理。

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Dim x(2) As Variant
Dim y(2) As Variant
Dim z(2) As Variant
Dim y_alpha As Double
y_alpha = Arcsin(Aabs_v(Dot(y, Array(1, 0, 0))))

'|Y|=1
y(0) = 0
y(1) = y(1) / Sqrt(y(1) ^ 2 + y(2) ^ 2)
y(2) = y(2) / Sqrt(y(1) ^ 2 + y(2) ^ 2)

Dim ar(2) As Variant '旋转轴向量
ar(0) = Cross(Array(Matrix.ArrayData(3), Matrix.ArrayData(4), Matrix.ArrayData(5)), y)(0)
ar(1) = Cross(Array(Matrix.ArrayData(3), Matrix.ArrayData(4), Matrix.ArrayData(5)), y)(1)
ar(2) = Cross(Array(Matrix.ArrayData(3), Matrix.ArrayData(4), Matrix.ArrayData(5)), y)(2)

Dim k As Single '转换为单位向量（模长为1）
k = 1 / Sqrt(ar(0) ^ 2 + ar(1) ^ 2 + ar(2) ^ 2)
ar(0) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(0)
ar(1) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(1)
ar(2) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(2)

'按罗德里格旋转公式算出XZ轴旋转后的向量
x(0) = Rodrigues(Array(Matrix.ArrayData(0), Matrix.ArrayData(1), Matrix.ArrayData(2)), ar, y_alpha)(0)
x(1) = Rodrigues(Array(Matrix.ArrayData(0), Matrix.ArrayData(1), Matrix.ArrayData(2)), ar, y_alpha)(1)
x(2) = Rodrigues(Array(Matrix.ArrayData(0), Matrix.ArrayData(1), Matrix.ArrayData(2)), ar, y_alpha)(2)
z(0) = Rodrigues(Array(Matrix.ArrayData(6), Matrix.ArrayData(7), Matrix.ArrayData(8)), ar, y_alpha)(0)
z(1) = Rodrigues(Array(Matrix.ArrayData(6), Matrix.ArrayData(7), Matrix.ArrayData(8)), ar, y_alpha)(1)
z(2) = Rodrigues(Array(Matrix.ArrayData(6), Matrix.ArrayData(7), Matrix.ArrayData(8)), ar, y_alpha)(2)

那么怎么转过去呢，不能直接对 Orientation3 赋值，需要用 CreateTransform 转换为矩阵向量对象，具体如下。

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'新的视角矩阵向量
Dim rotationArray(15) As Double
rotationArray(0) = x(0): rotationArray(1) = x(1): rotationArray(2) = x(2): rotationArray(13) = 1
rotationArray(3) = y(0): rotationArray(4) = y(1): rotationArray(5) = y(2): rotationArray(14) = 0
rotationArray(6) = z(0): rotationArray(7) = z(1): rotationArray(8) = z(2): rotationArray(15) = 0
rotationArray(9) = Matrix.ArrayData(9): rotationArray(10) = Matrix.ArrayData(10): rotationArray(11) = Matrix.ArrayData(11): rotationArray(12) = 1

Dim swMathUtil As SldWorks.MathUtility
Dim swTransform As SldWorks.MathTransform
Set swMathUtil = swApp.GetMathUtility
Set swTransform = swMathUtil.CreateTransform(rotationArray)
swModelView.Orientation3 = swTransform
swModel.GraphicsRedraw2 '刷新画面

完整代码

展开代码（点 Copy 可以复制）

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Option Explicit

Sub main()
    Dim swApp As SldWorks.SldWorks
    Dim swModel As SldWorks.ModelDoc2
    Dim swModelView As SldWorks.ModelView
    Dim viewMatrix As SldWorks.MathTransform
    Dim i As Integer

    Set swApp = Application.SldWorks
    Set swModel = swApp.ActiveDoc
    Set swModelView = swModel.ActiveView

    ' Orignal Orientation Martrix
    Set viewMatrix = swModelView.Orientation3
    Debug.Print "Orignal Orientation Martrix: "
    For i = 0 To 9 Step 3
        Debug.Print viewMatrix.ArrayData(i), viewMatrix.ArrayData(i + 1), viewMatrix.ArrayData(i + 2), viewMatrix.ArrayData(i / 3 + 12)
    Next i

    ' Determine the Most Appropriate Axis
    Dim x(2) As Variant
    Dim y(2) As Variant
    Dim z(2) As Variant
    Dim ar(2) As Variant
    Dim k As Double
    x(0) = viewMatrix.ArrayData(0)
    x(1) = viewMatrix.ArrayData(1)
    x(2) = viewMatrix.ArrayData(2)
    y(0) = viewMatrix.ArrayData(3)
    y(1) = viewMatrix.ArrayData(4)
    y(2) = viewMatrix.ArrayData(5)
    z(0) = viewMatrix.ArrayData(6)
    z(1) = viewMatrix.ArrayData(7)
    z(2) = viewMatrix.ArrayData(8)
    If viewMatrix.ArrayData(0) * viewMatrix.ArrayData(3) * viewMatrix.ArrayData(6) = 0 Then
        Debug.Print "No Need to Rotate"
        End
    End If
    ' Angle Between the Vector And the YZ Plane
    Dim x_alpha As Double
    Dim y_alpha As Double
    Dim z_alpha As Double
    x_alpha = Arcsin(Abs_v(Dot(x, Array(1, 0, 0))))
    y_alpha = Arcsin(Abs_v(Dot(y, Array(1, 0, 0))))
    z_alpha = Arcsin(Abs_v(Dot(z, Array(1, 0, 0))))
    Debug.Print Chr(10) & "Angle Between the Vector And the YZ Plane:", x_alpha, y_alpha, z_alpha
    ' min = X
    If x_alpha < y_alpha And x_alpha < z_alpha Then
        Debug.Print "X Rotation Angel: " & x_alpha
        x(0) = 0
        x(1) = x(1) / Sqrt(x(1) ^ 2 + x(2) ^ 2)
        x(2) = x(2) / Sqrt(x(1) ^ 2 + x(2) ^ 2)

        ar(0) = Cross(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), x)(0)
        ar(1) = Cross(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), x)(1)
        ar(2) = Cross(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), x)(2)
        k = 1 / Sqrt(ar(0) ^ 2 + ar(1) ^ 2 + ar(2) ^ 2)
        ar(0) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(0)
        ar(1) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(1)
        ar(2) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(2)

        y(0) = Rodrigues(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), ar, x_alpha)(0)
        y(1) = Rodrigues(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), ar, x_alpha)(1)
        y(2) = Rodrigues(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), ar, x_alpha)(2)
        z(0) = Rodrigues(Array(viewMatrix.ArrayData(6), viewMatrix.ArrayData(7), viewMatrix.ArrayData(8)), ar, x_alpha)(0)
        z(1) = Rodrigues(Array(viewMatrix.ArrayData(6), viewMatrix.ArrayData(7), viewMatrix.ArrayData(8)), ar, x_alpha)(1)
        z(2) = Rodrigues(Array(viewMatrix.ArrayData(6), viewMatrix.ArrayData(7), viewMatrix.ArrayData(8)), ar, x_alpha)(2)
    ' min = Y
    ElseIf y_alpha < x_alpha And y_alpha < z_alpha Then
        Debug.Print "Y Rotation Angel: " & y_alpha
        y(0) = 0
        y(1) = y(1) / Sqrt(y(1) ^ 2 + y(2) ^ 2)
        y(2) = y(2) / Sqrt(y(1) ^ 2 + y(2) ^ 2)

        ar(0) = Cross(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), y)(0)
        ar(1) = Cross(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), y)(1)
        ar(2) = Cross(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), y)(2)

        k = 1 / Sqrt(ar(0) ^ 2 + ar(1) ^ 2 + ar(2) ^ 2)
        ar(0) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(0)
        ar(1) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(1)
        ar(2) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(2)

        x(0) = Rodrigues(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), ar, y_alpha)(0)
        x(1) = Rodrigues(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), ar, y_alpha)(1)
        x(2) = Rodrigues(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), ar, y_alpha)(2)
        z(0) = Rodrigues(Array(viewMatrix.ArrayData(6), viewMatrix.ArrayData(7), viewMatrix.ArrayData(8)), ar, y_alpha)(0)
        z(1) = Rodrigues(Array(viewMatrix.ArrayData(6), viewMatrix.ArrayData(7), viewMatrix.ArrayData(8)), ar, y_alpha)(1)
        z(2) = Rodrigues(Array(viewMatrix.ArrayData(6), viewMatrix.ArrayData(7), viewMatrix.ArrayData(8)), ar, y_alpha)(2)
    ' min = Z
    Else
        Debug.Print "Z Rotation Angel: " & z_alpha
        z(0) = 0
        z(1) = z(1) / Sqrt(z(1) ^ 2 + z(2) ^ 2)
        z(2) = z(2) / Sqrt(z(1) ^ 2 + z(2) ^ 2)

        ar(0) = Cross(Array(viewMatrix.ArrayData(6), viewMatrix.ArrayData(7), viewMatrix.ArrayData(8)), z)(0)

        k = 1 / Sqrt(ar(0) ^ 2 + ar(1) ^ 2 + ar(2) ^ 2)
        ar(0) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(0)
        ar(1) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(1)
        ar(2) = Array(ar(0) * k, ar(1) * k, ar(2) * k)(2)

        x(0) = Rodrigues(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), ar, z_alpha)(0)
        x(1) = Rodrigues(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), ar, z_alpha)(1)
        x(2) = Rodrigues(Array(viewMatrix.ArrayData(0), viewMatrix.ArrayData(1), viewMatrix.ArrayData(2)), ar, z_alpha)(2)
        y(0) = Rodrigues(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), ar, z_alpha)(0)
        y(1) = Rodrigues(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), ar, z_alpha)(1)
        y(2) = Rodrigues(Array(viewMatrix.ArrayData(3), viewMatrix.ArrayData(4), viewMatrix.ArrayData(5)), ar, z_alpha)(2)
    End If

    Debug.Print Chr(10) & "Rotation Axis: ", ar(0), ar(1), ar(2)
    Debug.Print Chr(10) & "New Orientation Martrix: "
    Debug.Print x(0), x(1), x(2)
    Debug.Print y(0), y(1), y(2)
    Debug.Print z(0), z(1), z(2)

    Dim rotationArray(15) As Double
    rotationArray(0) = x(0): rotationArray(1) = x(1): rotationArray(2) = x(2): rotationArray(12) = 1
    rotationArray(3) = y(0): rotationArray(4) = y(1): rotationArray(5) = y(2): rotationArray(13) = 0
    rotationArray(6) = z(0): rotationArray(7) = z(1): rotationArray(8) = z(2): rotationArray(14) = 0
    rotationArray(9) = viewMatrix.ArrayData(9): rotationArray(10) = viewMatrix.ArrayData(10): rotationArray(11) = viewMatrix.ArrayData(11): rotationArray(15) = 0

    Dim swMathUtil As SldWorks.MathUtility
    Dim swTransform As SldWorks.MathTransform
    Set swMathUtil = swApp.GetMathUtility
    Set swTransform = swMathUtil.CreateTransform(rotationArray)
    swModelView.Orientation3 = swTransform
    swModel.GraphicsRedraw2

End Sub

'Rodrigues' rotation formula
Function Rodrigues(m As Variant, n As Variant, alpha As Double) As Variant

    Rodrigues = Array(m(0) * Cos(alpha) + Sin(alpha) * Cross(n, m)(0) + (1 - Cos(alpha)) * Dot(n, Dot(n, m))(0), m(1) * Cos(alpha) + Sin(alpha) * Cross(n, m)(1) + (1 - Cos(alpha)) * Dot(n, Dot(n, m))(1), m(2) * Cos(alpha) + Sin(alpha) * Cross(n, m)(2) + (1 - Cos(alpha)) * Dot(n, Dot(n, m))(2))

End Function

'Cross
Function Cross(m As Variant, n As Variant) As Variant

    Cross = Array(m(1) * n(2) - m(2) * n(1), m(2) * n(0) - m(0) * n(2), m(0) * n(1) - m(1) * n(0))

End Function

'Dot
Function Dot(m As Variant, n As Variant) As Variant

    Dot = Array(m(0) * n(0), m(1) * n(1), m(2) * n(2))

End Function

'Abs
Function Abs_v(v As Variant) As Double

    Abs_v = Sqrt(v(0) ^ 2 + v(1) ^ 2 + v(2) ^ 2)

End Function

许可协议

本文采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处，谢谢！

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