AMCAX Kernel
Geometry kernel for CAD/CAE/CAM
九韶内核 1.0.0.0
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如何多次复合相同类型的变换

概述

本教程提供了如何在 Transformation3 中，设置多次相同类型的变换，并且每个变换都能生效的方法。

方法

首先，我们先讲一个错误案例。在下面代码中，只有第三次 SetRotation 起作用，前两个都是无效的。

//Make box
AMCAX::MakeBox mkbox = AMCAX::MakeBox(AMCAX::Point3(0., 0., 0.), AMCAX::Point3(1., 2., 3.));
AMCAX::TopoShape shape = mkbox.Shape();
//SetRotation
AMCAX::Transformation3 trsf;
trsf.SetRotation(AMCAX::CartesianCoordinateSystem::OX(), AMCAX::Constants::pi / 3.);
trsf.SetRotation(AMCAX::CartesianCoordinateSystem::OY(), AMCAX::Constants::pi / 3.);
trsf.SetRotation(AMCAX::CartesianCoordinateSystem::OZ(), AMCAX::Constants::pi / 3.);
//Get a shape with a transformation
shape = AMCAX::TransformShape(shape, trsf);
//Write
AMCAX::STEP::StepDataTool::Write(shape, "./test_box1.step");
AMCAX::CartesianCoordinateSystem::OZ
static AMCAX_API const Axis3 & OZ() noexcept
获取三维中的 z 轴，包括原点和 z 轴方向
AMCAX::CartesianCoordinateSystem::OX
static AMCAX_API const Axis3 & OX() noexcept
获取三维中的 x 轴，包括原点和 x 轴方向
AMCAX::CartesianCoordinateSystem::OY
static AMCAX_API const Axis3 & OY() noexcept
获取三维中的 y 轴，包括原点和 y 轴方向
AMCAX::MakeBox
创建立方体的类
定义 MakeBox.hpp:18
AMCAX::MakeShape::Shape
virtual AMCAX_API const TopoShape & Shape()
获取结果形状
AMCAX::STEP::StepDataTool::Write
static AMCAX_API bool Write(const AMCAX::TopoShape &s, std::ostream &os)
Write a TopoShape to a stream in STEP format.
AMCAX::TopoShape
形状的基类，包含具有位置和方向信息的基础形状
定义 TopoShape.hpp:15
AMCAX::TransformShape
对形状进行变换的类
定义 TransformShape.hpp:12
AMCAX::TransformationT::SetRotation
void SetRotation(const PointT< OtherScalar, DIM > &point, const OtherScalar2 &angle) noexcept
设置变换为二维中绕点旋转某一角度
定义 TransformationT.hpp:138
AMCAX::Constants::pi
constexpr double pi
数学常数 Pi，圆的周长与直径之比
定义 Constants.hpp:42
AMCAX::Transformation3
TransformationT< double, 3 > Transformation3
三维变换
定义 TransformationT.hpp:1102
AMCAX::Point3
PointT< double, 3 > Point3
三维点
定义 PointT.hpp:459

那么如果希望三次 SetRotation 都可以起作用，可以通过以下几种方式。

执行一次 TransformShape：右乘

//Make box
AMCAX::MakeBox mkbox = AMCAX::MakeBox(AMCAX::Point3(0., 0., 0.), AMCAX::Point3(1., 2., 3.));
AMCAX::TopoShape shape = mkbox.Shape();
//SetRotation
AMCAX::Transformation3 trsf1;
trsf1.SetRotation(AMCAX::CartesianCoordinateSystem::OX(), AMCAX::Constants::pi / 3.);
AMCAX::Transformation3 trsf2;
trsf2.SetRotation(AMCAX::CartesianCoordinateSystem::OY(), AMCAX::Constants::pi / 3.);
AMCAX::Transformation3 trsf3;
trsf3.SetRotation(AMCAX::CartesianCoordinateSystem::OZ(), AMCAX::Constants::pi / 3.);
AMCAX::Transformation3 finalTrsf;
finalTrsf = trsf3 * trsf2 * trsf1;
//Get a shape with a transformation
shape = AMCAX::TransformShape(shape, finalTrsf);
//Write
AMCAX::STEP::StepDataTool::Write(shape, "./test_box3.step");

执行一次 TransformShape：左乘

//Make box
AMCAX::MakeBox mkbox = AMCAX::MakeBox(AMCAX::Point3(0., 0., 0.), AMCAX::Point3(1., 2., 3.));
AMCAX::TopoShape shape = mkbox.Shape();
//SetRotation
AMCAX::Transformation3 trsf1;
trsf1.SetRotation(AMCAX::CartesianCoordinateSystem::OX(), AMCAX::Constants::pi / 3.);
AMCAX::Transformation3 trsf2;
trsf2.SetRotation(AMCAX::CartesianCoordinateSystem::OY(), AMCAX::Constants::pi / 3.);
AMCAX::Transformation3 trsf3;
trsf3.SetRotation(AMCAX::CartesianCoordinateSystem::OZ(), AMCAX::Constants::pi / 3.);
AMCAX::Transformation3 finalTrsf;
finalTrsf = trsf1.LeftMultiplied(trsf2).LeftMultiplied(trsf3);
//Get a shape with a transformation
shape = AMCAX::TransformShape(shape, finalTrsf);
//Write
AMCAX::STEP::StepDataTool::Write(shape, "./test_box4.step");
AMCAX::TransformationT::LeftMultiplied
constexpr TransformationT LeftMultiplied(const TransformationT< OtherScalar, DIM > &other) const noexcept
获取左乘其他变换后的变换
定义 TransformationT.hpp:893

执行多次 TransformShape

//Make box
AMCAX::MakeBox mkbox = AMCAX::MakeBox(AMCAX::Point3(0., 0., 0.), AMCAX::Point3(1., 2., 3.));
AMCAX::TopoShape shape = mkbox.Shape();
//SetRotation
AMCAX::Transformation3 trsf;
trsf.SetRotation(AMCAX::CartesianCoordinateSystem::OX(), AMCAX::Constants::pi / 3.);
shape = AMCAX::TransformShape(shape, trsf);
trsf.SetRotation(AMCAX::CartesianCoordinateSystem::OY(), AMCAX::Constants::pi / 3.);
shape = AMCAX::TransformShape(shape, trsf);
trsf.SetRotation(AMCAX::CartesianCoordinateSystem::OZ(), AMCAX::Constants::pi / 3.);
//Get a shape with a transformation
shape = AMCAX::TransformShape(shape, trsf);
//Write
AMCAX::STEP::StepDataTool::Write(shape, "./test_box2.step");