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、1、 贝塞尔曲线的拼接用matlab画代码如下：% By lyqmathclc; 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);endplot(r(1,:),r(2,:),p(1,:),p(2,:),'-or')2、 B样条曲线的正算function Byt8(p0,p1,p2,p3,p4,p5,p6

2、,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) p1(1) p2(

3、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) p

4、1(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). +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;%plot

5、(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)*t

6、.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)

7、*(1/6)*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)3、 B样条曲线的反算function Byangtiao8(p)t=0:0.005:1;hold onfo

8、r 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;plot(x,y,'k');endplot(p(1,1) p(1,2) p(1,

9、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); 4、 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 "

10、TestDoc.h"#include "TestView.h"#ifdef _DEBUG#define new DEBUG_NEW#undef THIS_FILEstatic char THIS_FILE = _FILE_;#endif/ CTestViewIMPLEMENT_DYNCREATE(CTestView, CView)BEGIN_MESSAGE_MAP(CTestView, CView)/AFX_MSG_MAP(CTestView)ON_COMMAND(ID_MENUDrawHermite, OnMENUDrawHermite)/AFX_MSG_MAP

11、/ Standard printing commandsON_COMMAND(ID_, CView:On)ON_COMMAND(ID_, CView:On)ON_COMMAND(ID_, CView:On)END_MESSAGE_MAP()/ CTestView construction/destructionCTestView:CTestView()/ TODO: add construction code here/9个型值点的初始化p100=410;p101=532;p110=210;p111=386;p120=410;p121=316;p130=310;p131=162;p140=51

12、0;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=-100;p261=100;p270=-100;p271=100;p280=-100;p281=-100;CTestView:CTestView()BOOL CTestVi

13、ew:PreCreateWindow(CREATESTRUCT& cs)/ TODO: Modify the Window class or styles here by modifying/ the CREATESTRUCT csreturn CView:PreCreateWindow(cs);/ CTestView drawingvoid CTestView:OnDraw(CDC* pDC)CTestDoc* pDoc = GetDocument();ASSERT_VALID(pDoc);/ TODO: add draw code for native data hereCPen

14、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;i<9;i+)pDC->LineTo(p1i0,p1i1);pDC->Ellipse(p1i0-2,p1i1-2,p1i0+2,p1i1+2);pDC->SelectObjec

15、t(pOldPen);MyPen.DeleteObject();/ CTestView printingBOOL CTestView:OnPreparePrinting(CPrintInfo* pInfo)/ default preparationreturn DoPreparePrinting(pInfo);void CTestView:OnBeginPrinting(CDC* /*pDC*/, CPrintInfo* /*pInfo*/)/ TODO: add extra initialization before printingvoid CTestView:OnEndPrinting(

16、CDC* /*pDC*/, CPrintInfo* /*pInfo*/)/ TODO: add cleanup after printing/ CTestView diagnostics#ifdef _DEBUGvoid CTestView:AssertValid() constCView:AssertValid();void CTestView:Dump(CDumpContext& dc) constCView:Dump(dc);CTestDoc* CTestView:GetDocument() / non-debug version is inlineASSERT(m_pDocum

17、ent->IsKindOf(RUNTIME_CLASS(CTestDoc);return (CTestDoc*)m_pDocument;#endif /_DEBUG/ CTestView message handlersvoid CTestView:Hermite(CDC *pDC)/绘制Hermite三次插值样条int a44 =2,-2,1,1,-3,3,-2,-1,0,0,1,0,1,0,0,0;/Mh矩阵系数int b42;/边界点 for(int i=0;i<8;i+)b00=p1i0;b01=p1i1;/起点的坐标b10=p1i+10;b11=p1i+11;/终点的坐标

18、b20=p2i0;b21=p2i1;/起点的导数b30=p2i+10;b31=p2i+11;/终点的导数MultiMatrix(a,b);CPen MyPen,*pOldPen;MyPen.CreatePen(PS_SOLID,1,RGB(255,0,0);pOldPen=pDC->SelectObject(&MyPen);pDC->MoveTo(p1i0,p1i1);for(double t=0.0;t<=1;t+=1.0/400)int x=ROUND(pow(t,3)*result00+pow(t,2)*result10+ t*result20+result30);int y=ROUND(pow(t,3)*result01+pow(t,2)*result11+ t*result21+result31);pDC->LineTo(x,y);pDC->SelectObject(pOldPen);MyPen.DeleteObject();void CTestView:MultiMatrix(int a44,int b42)/矩阵相乘int i,j,k;for(i=0;i<4;i+)for(