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=li nspace(0,1,200);n=size(p,2)-1;r=0;for k=0:nr=r+prod(1: n)/(prod(1:k)*prod(1: n-k)*p(:,k+1)*(t4k.*(1-t).A( 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,p7)t=0:0.001

2、:1;%m=-1 3 -3 1;3 -6 3 0;-3 0 3 0;1 4 1 0;x=p0(1)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p1(1)*(1/6)*(3*t.A3-6*t.A2+4)+p2(1)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p3(1)*(1/6)*t.A3;y=p0(2)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p1(2)*(1/6)*(3*t.A3-6*t.A2+4)+p2(2)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p3(2)*(1/6)*t.A3;%plot(p0(1) p1(1) p2(1)

3、p3(1),p 0(2) p1(2) p2(2) p3( 2);hold on;plot(x,y, r);x=p1(1)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p2(1)*(1/6)*(3*t.A3-6*t.A2+4)+p3(1)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p4(1)*(1/6)*t.A3;y=p1(2)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p2(2)*(1/6)*(3*t.A3-6*t.A2+4)+p3(2)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p4(2)*(1/6)*t.A3;%plot(p0(1) p

4、1(1) p2(1) p3(1),p 0(2) p1(2) p2(2) p3( 2);hold on;plot(x,y, r);x=p2(1)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p3(1)*(1/6)*(3*t.A3-6*t.A2+4)+p4(1)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p5(1)*(1/6)*t.A3;y=p2(2)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p3(2)*(1/6)*(3*tA3-6*tA2+4)+p4(2)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p5(2)*(1/6)*t.A3;%plo

5、t(pO p1(1) p2(1) p3(1),p 0(2) p1(2) p2(2) p3( 2);hold on;plot(x,y, r);x=p3(1)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p4(1)*(1/6)*(3*t.A3-6*t.A2+4) +p5(1)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p6(1)*(1/6)*t.A3;y=p3(2)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p4(2)*(1/6)*(3*t.A3-6*t.A2+4)+p5(2)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p6(2)*(1/6)*

6、t.A3;%plot(pO(1) p1(1) p2(1) p3(1),p 0(2) p1(2) p2(2) p3( 2);hold on;plot(x,y, r);x=p4(1)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p5(1)*(1/6)*(3*tA3-6*tA2+4) +p6(1)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p7(1)*(1/6)*t.A3;y=p4(2)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p5(2)*(1/6)*(3*t.A3-6*t.A2+4)+p6(2)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p7

7、(2)*(1/6)*t.A3;%plot(pO(1) p1(1) p2(1) p3(1),p 0(2) p1(2) p2(2) p3( 2);hold on;p1(2)p2(2)p3(2)plot(x,y, r);plot(pO(1) p1(1)p2(1)p3(1)p4(1)p5(1)p6(1)p7(1),p 0(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)02468101298765432103、B样条曲线的反算function Byangtiao8(p)t=0:0.005:1;hold onfor

8、i=1:5x=p(1,i)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p(1,i+1)*(1/6)*(3*t.A3-6*t.A2+4) +p(1,i+2)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p(1,i+3)*(1/6)*t.A3;y=p(2,i)*(1/6)*(-t.A3+3*t.A2-3*t+1)+p(2,i+1)*(1/6)*(3*t.A3-6*t.A2+4)+p(2,i+2)*(1/6)*(-3*t.A3+3*t.A2+3*t+1)+p(2,i+3)*(1/6)*t.A3;plot(x,y, k);endplot(p(1,1) p(1,2) p(1,3

9、) 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 : impleme ntati on of the CTestView class/#include stdafx.h#i nclude 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 TestView.h#ifdef _DEBU

10、G#defi ne new DEBUG_NEW#un def THIS_FILEstatic char THIS_FILE = _FILE_;#en dif/ CTestViewIMPLEMENT_DYNCREATE(CTestView, CView)BEGIN_MESSAGE_MAP(CTestView, CView) AFX_MSG_MAP(CTestView)ON_COMMAND(ID_MENUDrawHermite, On MENUDrawHermite) AFX_MSG_MAP/ Stan dard prin ti ng comma ndsON_COMMAND(ID_FILE_PRI

11、NT, CView:O nFilePri nt)ON_COMMAND(ID_FILE_PRINT_DIRECT, CView:O nFilePri nt) ON_COMMAND(ID_FILE_PRINT_PREVIEW, CView:O nF ilePri ntPreview) END_MESSAGE_MAP()/ CTestView con structio n/destructio nCTestView:CTestView()/ TODO: add con struct ion code here9个型值点的初始化p100=410;p101=532;p110=210;p111=386;p

12、120=410;p121=316;p130=310;p131=162;p140=510;p141=50;p150=710;p151=162;p1 60=610;p1 61=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;p2 5 1=100;p2 60=-100;p2 6 1=100;p270=-100;p271=100;p280=

13、-100;p281=-100;CTestView:CTestView()BOOL CTestView:PreCreateWi ndow(CREATESTRUCT & cs)/ TODO: Modify the Window class or styles here by modifyi ng/ the CREATESTRUCT csreturn CView:PreCreateWi ndow(cs);/ CTestView draw ingvoid CTestView:O nDraw(CDC* pDC)CTestDoc* pDoc = GetDocume nt();ASSERT_VALID(pD

14、oc);/ TODO: add draw code for n ative data hereCPen MyPe n,*pOldPe n;MyPen.CreatePen(PS_SOLID,3,RGB(O,O,255); 蓝色笔绘制特征多边形pOldPe n=pDC-SelectObject(&MyPe n);pDC-MoveTo(p100,p101);pDC-Ellipse(p100-2,p101-2,p100+2,p101+2); 绘制特征多边形顶点for(i nt i=1;iLi neTo(p1i0,p1i1);pDC-Ellipse(p1i0-2,p1i1-2,p1i0+2,p1i1+2

15、);pDC-SelectObject(pOldPe n);MyPe n.DeleteObject();/ CTestView printingBOOL CTestView:O nPreparePri ntin g(CPri ntI nfo* pI nfo)/ default preparati onreturn DoPreparePri nti ng(pl nfo);void CTestView:O nBegi nPrintin g(CDC* /*pDC*/, CPrintlnfo* /*pI nfo*/)/ TODO: add extra in itializati on before pr

16、intingvoid CTestView:O nEn dPri ntin g(CDC* /*pDC*/, CPri ntlnfo* /*pI nfo*/)/ TODO: add clea nup after printing/ CTestView diag no stics#ifdef _DEBUGvoid CTestView:AssertValid() constCView:AssertValid();void CTestView:Dump(CDumpC on text & dc) constCView:Dump(dc);CTestDoc* CTestView:GetDocume nt()

17、/ non-debug version is inlineASSERT(m_pDocume nt-lsKi ndOf(RUNTIME_CLASS(CTestDoc); return (CTestDoc*)m_pDocume nt;#endif /_DEBUG/ CTestView message han dlersvoid 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(i nt i=0;iSelectObject(&M yPe n); pDC-MoveTo(p1i0,p1i1);for(