整理B样条曲线正算反算贝塞尔曲线拼接曲面车身CAD作业答案

1、精品文档 1、 贝塞尔曲线的拼接 画用matlab代码如下： % By lyqmath clc; clear all; close all; p=1 2; 4 8; 6 15; 9 18; p=p; t=linspace(0,1,200); n=size(p,2)-1; r=0; for k=0:n r=r+prod(1:n)/(prod(1:k)*prod(1:n-k)*p(:,k+1)*(t.k.*(1-t).(n-k); end plot(r(1,:),r(2,:),p(1,:),p(2,:),-or) 5、B样条曲线的正算 function Byt8(p0,p1,p2,p3,p4,p5

2、,p6,p7) t=0:0.001:1; %m=-1 3 -3 1;3 -6 3 0;-3 0 3 0;1 4 1 0; x=p0(1)*(1/6)*(-t.3+3*t.2-3*t+1)+p1(1)*(1/6)*(3*t.3-6*t.2+4). +p2(1)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p3(1)*(1/6)*t.3; y=p0(2)*(1/6)*(-t.3+3*t.2-3*t+1)+p1(2)*(1/6)*(3*t.3-6*t.2+4). +p2(2)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p3(2)*(1/6)*t.3; %plot(p0(1) p

3、1(1) p2(1) p3(1),p0(2) p1(2) p2(2) p3(2); hold on; plot(x,y,r); x=p1(1)*(1/6)*(-t.3+3*t.2-3*t+1)+p2(1)*(1/6)*(3*t.3-6*t.2+4). +p3(1)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p4(1)*(1/6)*t.3; y=p1(2)*(1/6)*(-t.3+3*t.2-3*t+1)+p2(2)*(1/6)*(3*t.3-6*t.2+4). +p3(2)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p4(2)*(1/6)*t.3; %plot(p0(1

4、) p1(1) p2(1) p3(1),p0(2) p1(2) p2(2) p3(2); hold on; plot(x,y,r); x=p2(1)*(1/6)*(-t.3+3*t.2-3*t+1)+p3(1)*(1/6)*(3*t.3-6*t.2+4). 精品文档精品文档 +p4(1)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p5(1)*(1/6)*t.3; y=p2(2)*(1/6)*(-t.3+3*t.2-3*t+1)+p3(2)*(1/6)*(3*t.3-6*t.2+4). +p4(2)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p5(2)*(1/6)*t.3

5、; %plot(p0(1) p1(1) p2(1) p3(1),p0(2) p1(2) p2(2) p3(2); hold on; plot(x,y,r); x=p3(1)*(1/6)*(-t.3+3*t.2-3*t+1)+p4(1)*(1/6)*(3*t.3-6*t.2+4). +p5(1)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p6(1)*(1/6)*t.3; y=p3(2)*(1/6)*(-t.3+3*t.2-3*t+1)+p4(2)*(1/6)*(3*t.3-6*t.2+4). +p5(2)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p6(2)*(1/6)*

6、t.3; %plot(p0(1) p1(1) p2(1) p3(1),p0(2) p1(2) p2(2) p3(2); hold on; plot(x,y,r); x=p4(1)*(1/6)*(-t.3+3*t.2-3*t+1)+p5(1)*(1/6)*(3*t.3-6*t.2+4). +p6(1)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p7(1)*(1/6)*t.3; y=p4(2)*(1/6)*(-t.3+3*t.2-3*t+1)+p5(2)*(1/6)*(3*t.3-6*t.2+4). +p6(2)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p7(2)*(1/

7、6)*t.3; %plot(p0(1) p1(1) p2(1) p3(1),p0(2) p1(2) p2(2) p3(2); hold on; plot(x,y,r); plot(p0(1) p1(1) p2(1) p3(1) p4(1) p5(1) p6(1) p7(1),p0(2) p1(2) p2(2) p3(2) p4(2) p5(2) p6(2) p7(2); 执行： Byt8(0,0,1,4,3,9,5,7,6,2,7,6,9,5,11,3) 9 876543210024681012 6、B样条曲线的反算 function Byangtiao8(p) t=0:0.005:1; ho

8、ld on for i=1:5 x=p(1,i)*(1/6)*(-t.3+3*t.2-3*t+1)+p(1,i+1)*(1/6)*(3*t.3-6*t.2+4). +p(1,i+2)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p(1,i+3)*(1/6)*t.3; y=p(2,i)*(1/6)*(-t.3+3*t.2-3*t+1)+p(2,i+1)*(1/6)*(3*t.3-6*t.2+4). +p(2,i+2)*(1/6)*(-3*t.3+3*t.2+3*t+1)+p(2,i+3)*(1/6)*t.3; 精品文档精品文档 plot(x,y,k); end plot(p(1,1)

9、p(1,2) p(1,3) p(1,4) p(1,5) p(1,6) p(1,7) p(1,8),p(2,1) p(2,2) p(2,3) p(2,4) p(2,5) p(2,6) p(2,7) p(2,8); 7、双三次B样条曲面的算法 / TestView.cpp : implementation of the CTestView class / #include stdafx.h #include Test.h #define ROUND(a) int(a+0.5)/四舍五入 #include math.h/数学头文件 #include TestDoc.h #include TestVi

10、ew.h #ifdef _DEBUG #define new DEBUG_NEW #undef THIS_FILE static char THIS_FILE = _FILE_; #endif / / CTestView IMPLEMENT_DYNCREATE(CTestView, CView) BEGIN_MESSAGE_MAP(CTestView, CView) /AFX_MSG_MAP(CTestView) ON_COMMAND(ID_MENUDrawHermite, OnMENUDrawHermite) 精品文档精品文档 /AFX_MSG_MAP / Standard printing

11、 commands ON_COMMAND(ID_FILE_PRINT, CView:OnFilePrint) ON_COMMAND(ID_FILE_PRINT_DIRECT, CView:OnFilePrint) ON_COMMAND(ID_FILE_PRINT_PREVIEW, CView:OnFilePrintPreview) END_MESSAGE_MAP() / / CTestView construction/destruction CTestView:CTestView() / TODO: add construction code here /9个型值点的初始化 p100=410

12、;p101=532; p110=210;p111=386; p120=410;p121=316; p130=310;p131=162; p140=510;p141=50; p150=710;p151=162; p160=610;p161=316; p170=810;p171=386; p180=610;p181=532; /9个型值点导数的初始化 p200=100;p201=-100; p210=100;p211=-100; p220=100;p221=-100; p230=100;p231=-100; p240=-100;p241=-100; p250=-100;p251=100; p260

13、=-100;p261=100; p270=-100;p271=100; p280=-100;p281=-100; CTestView:CTestView() BOOL CTestView:PreCreateWindow(CREATESTRUCT& cs) / TODO: Modify the Window class or styles here by modifying / the CREATESTRUCT cs return CView:PreCreateWindow(cs); 精品文档精品文档 / / CTestView drawing void CTestView:OnDraw(CDC

14、* pDC) CTestDoc* pDoc = GetDocument(); ASSERT_VALID(pDoc); / TODO: add draw code for native data here CPen MyPen,*pOldPen; MyPen.CreatePen(PS_SOLID,3,RGB(0,0,255);/蓝色笔绘制特征多边形 pOldPen=pDC-SelectObject(&MyPen); pDC-MoveTo(p100,p101); pDC-Ellipse(p100-2,p101-2,p100+2,p101+2);/绘制特征多边形顶点 for(int i=1;iLin

15、eTo(p1i0,p1i1); pDC-Ellipse(p1i0-2,p1i1-2,p1i0+2,p1i1+2); pDC-SelectObject(pOldPen); MyPen.DeleteObject(); / / CTestView printing BOOL CTestView:OnPreparePrinting(CPrintInfo* pInfo) / default preparation return DoPreparePrinting(pInfo); void CTestView:OnBeginPrinting(CDC* /*pDC*/, CPrintInfo* /*pInf

16、o*/) / TODO: add extra initialization before printing void CTestView:OnEndPrinting(CDC* /*pDC*/, CPrintInfo* /*pInfo*/) / TODO: add cleanup after printing / 精品文档 精品文档/ CTestView diagnostics #ifdef _DEBUG void CTestView:AssertValid() const CView:AssertValid(); void CTestView:Dump(CDumpContext& dc) co

17、nst CView:Dump(dc); CTestDoc* CTestView:GetDocument() / non-debug version is inline ASSERT(m_pDocument-IsKindOf(RUNTIME_CLASS(CTestDoc); return (CTestDoc*)m_pDocument; #endif /_DEBUG / / CTestView message handlers Hermite三次插值样条void CTestView:Hermite(CDC *pDC)/绘制 0,0,0;/Mh矩阵系数 int b42;/边界点 for(int i=0;iSelectObject(&MyPen); pDC-MoveTo(p1i0,p1i1); for(double t=0.0;tLineTo(x,y); 精品文档精品文档 pDC-SelectObject(pOldPen); MyPen.DeleteObject(); void CTestView:MultiMatrix(int a44,int b42)/矩阵相乘 int