NURBS插值插补.rar_B样条_插值_有理b样条_样条_非均匀插值

tic%%%%计算时间 clear cla reset; NURBS_ORDER=3; K=3; %q=[0 0; 4 3; 7 1; 9 5; 12 2; 16 5 ];%%输入曲线上点坐标 %q=[0 0; 4 3; 7 1; 9 5; 12 2; 16 5 ];%%输入曲线上点坐标 %q=[80 120; 110 80; 160 80; 120 40; 130 0; 80 30; 30 0;40 40; 0 80; 50 80; 80 120 ];%%输入曲线上点坐标 %q=[ 80 120; 110 80; 160 80; 120 40; 130 0; 80 30; 30 0; 40 40; 0 80 ;50 80; 80 120 ]; %五角星 % q=[ 54.493,52.139 ; 55.507,52.139 ; 56.082,49.615 ; 56.780,44.971 ; 69.575, 51.358 ; 77.786, 58.573; 90.526,67.081; 105.973,63.801; 100.400, 47.326; 94.567,39.913; 92.396, 30.485; % 83.440,33.757 ; 91.892,28.509 ; 89.444,20.393 ; 83.218,15.446 ; 87.621,4.830 ; 80.945, 9.267 ; 79.834,14.535; 76.074,8.522 ; 70.183,12.550 ; 64.171,16.865; 59.993, 22.122 ; % 55.680,36.359 ; 56.925,24.995 ; 59.765,19.828 ; 54.493,14.940 ; 49.220,19.828 ; 52.060,24.992 ; 53.305,36.359; 48.992,22.122; 44.814,16.865 ; 38.802,12.551; 32.911,8.521 ; % 29.152,14.535 ; 28.040,9.267 ; 21.364,4.830 ; 25.768,15.447 ; 19.539,20.391 ; 17.097, 28.512 ; 25.537,33.750; 16.602,30.496 ; 14.199, 39.803 ; 8.668,47.408 ; 3.000,63.794 ; % 18.465, 67.084 ; 31.197,58.572 ; 39.411,51.358 ; 52.204,44.971; 52.904,9.6140 ; 53.478,52.139; 54.493,52.139 ]; %%%%%%蝴蝶曲线 X=[0.0; 1.014; 1.589; 2.287; 15.082; 23.293; 36.033; 51.480;... 45.907; 40.074; 37.876; 28.947; 37.399; 34.951; 28.725;... 33.128; 26.452; 25.341; 21.581; 15.690; 9.678; 5.500; 1.187;... 2.432; 5.272; 0.0; -5.273; -2.433; -1.188; -5.501; -9.679; -15.691;... -21.582; -25.341; -26.453; -33.129; -28.725; -34.954; -37.396; -28.956;... -37.891; -40.294; -45.825; -51.493; -36.028; -23.296; -15.082; -2.289; -1.589; -1.015; 0.0]; Y=[0.0; 0.0; -2.524; -7.168; -0.781; 6.434; 14.942; 11.662; -4.813;... -12.226; -21.654; -18.382; -23.630; -31.746; -36.693; -47.309;... -42.872; -37.604; -43.617; -39.589; -35.274; -30.017; -15.780;... -27.144; -32.311; -37.199; -32.311; -27.145; -15.780; -30.017;... -35.274; -39.588; -43.618; -37.604; -42.872; -47.309; -36.692;... -31.748; -23.627; -18.389; -21.643; -12.336; -4.731; 11.655; 14.945;... 6.433; -0.781; -7.168; -2.524; 0.0; 0.0]; for i=1:length(X) q(i ,1)=X(i); q(i ,2)=Y(i); end %%%%扇叶%%%%%%%% % X = [ -16.0688, -0.0562, 7.8712, 13.5113, 15.0488, 13.5863, 9.1125, 8.2125,... % 8.4150, 9.2025, 10.5413, 12.0825, 13.5825, 15.1650, 18.1950, 25.5900, 31.6463,... % 34.3387, 37.6013, 41.3325, 45.1275, 49.6200, 56.9850, 57.1575, 54.1838, 48.1388,... % 39.2062, 30.1613, 15.1537, 11.8650, 10.4175, 9.0300, 8.3963, 8.3438, 8.5313,... % 9.0975, 10.6463, 18.3188, 27.3038, 30.2400, 32.4675, 33.5887, 33.2400, 30.2137,... % 16.0688, 0.0562, -7.8712, -13.5113, -15.0488, -13.5863, -9.1125, -8.2125, -8.4150,... % -9.2025, -10.5413, -12.0825, -13.5825, -15.1650, -18.1950, -25.5900, -31.6463,... % -34.3387, -37.6013, -41.3325, -45.1275, -49.6200, -56.9850, -57.1575, -54.1838,... % -48.1388, -39.2062, -30.1613, -15.1537, -11.8650, -10.4175, -9.0300, -8.3963, -8.3438,... % -8.5313, -9.0975, -10.6463, -18.3188, -27.3038, -30.2400, -32.4675, -33.5887, -33.2400,... % -30.2137, -16.0688]; % Y = [ -56.9850, -57.1575, -54.1838, -48.1388, -39.2062, -30.1613, -15.1537,... % - 11.8650, -10.4175, -9.0300, -8.3963, -8.3438, -8.5313, -9.0975, -10.6463, -18.3188,... % -27.3038, -30.2400, -32.4675, -33.5887, -33.2400, -30.2137, -16.0688, -0.0562, 7.8712,... % 13.5113, 15.0488, 13.5863, 9.1125, 8.2125, 8.4150, 9.2025, 10.5413, 12.0825,... % 13.5825, 15.1650, 18.1950, 25.5900, 31.6463, 34.3387, 37.6013, 41.3325, 45.1275,... % 49.6200, 56.9850, 57.1575, 54.1838, 48.1388, 39.2062, 30.1613, 15.1537, 11.8650,... % 10.4175, 9.0300, 8.3963, 8.3438, 8.5313, 9.0975, 10.6463, 18.3188, 27.3038,... % 30.2400, 32.4675, 33.5887, 32.400, 30.2137, 16.0688, 0.0562, -7.8712, -13.5113,... % -15.0488, -13.5863, -9.1125, -8.2125, -8.4150, -9.2025, -10.5413, -12.0825, -13.5825,... % -15.1650, -18.1950, -25.5900, -31.6463, -34.3387, -37.6013, -41.3325, -45.1275,... % -49.6200, -56.9850]; % for i=1:length(X) % q(i ,1)=X(i); % q(i ,2)=Y(i); % end %%%%%%%%%%%%%%%%%%%% % X=[ 0, -0.5, -0.707105, -0.866, -1, -0.866, -0.707105, -0.5, 0, 0.5, 0.707105, 0.866, 1 ,0.866, 0.707105, 0.5, 0]; % Y=[ 1, 0.866, 0.707105, 0.5, 0, -0.5, -0.707105, -0.866, -1, -0.866, -0.707105, -0.5 , 0 ,0.5, 0.707105 ,0.866, 1]; X=[ 0, 4, 6, 8 ]; Y=[ 0, 6, 4, 5 ]; %%%%%%%%%%%% %法向量n=（A,B，C）,过（x0,y0,z0） A=1; B=1; C=-1 x0=0; y0=0; z0=0; for i=1 : 1 : length(X) q(i ,3)=-A*(X(i )-x0)/C -B*( Y(i)-y0 )/C +z0; Z(i) = q(i ,3); end %%%%%%%%%%%%五角星%%%%%% % X=[0, 5.88, -9.51, 9.51, -5.88, 0]; % Y=[0, -18.09, -6.91, -6.91, -18.09, 0]; % Z=[0, -12.21, -16.42, 2.60, -23.97, 0 ]; %%%%%%%%%%%%%%%%%%%% for i=1:length(X) q(i ,1)=X(i); q(i ,2)=Y(i); q(i ,3)=Z(i); end %m+1型值点Q0,Q1,Q2...Qm,构造k次样条，需要m+k个控制点，形成m段曲线，每段曲线对应两个节点矢量，节点矢量个数m+1 %对于首末k+1次重复度节点，节点矢量个数为m+1+2k m=numel(q)/3-1; W=ones(m+K,1); l=zeros(m,1); for i=1:m; l(i)=((q(i+1,1)-q(i,1))^2+ (q(i+1,2)-q(i,2))^2 + (q(i+1,3)-q(i,3))^2 )^0.5; %计算弦长 end hel=sum(l);%累加弦长 U=zeros(m+1+2*K, 1); for i=1:m; U(4+i)=sum( l(1:i) ) / hel; end U(m+4:m+1+2*K)=1;%%构造n+p+1个节点矢量 for i=1 : 1 : (m+2*K) detal1(i)=U(i+1)-U(i); end for i=1 : 1 : (m+2*K - 1) detal2(i)=U(i+2)-U(i); end for i=1 : 1 : (m+2*K - 2) detal3(i)=U(i+3)-U(i); end for j=3 : 1 : m+3 i=j+1; a(i-2) = W(i-3) * detal1(i) * detal1(i) / ( detal2(i-1) * detal3(i-2) ); b(i-2) = W(i-2) * ( 1- detal1(i) * detal1(i) / ( detal2(i-1) * detal3(i-2) ) - detal1(i-1) * detal1(i-1) / ( detal2(i-1) * detal3(i-1) ) ); c(i-2) = W(i-1) * detal1(i-1) * detal1(i-1) / ( detal2(i-1) * detal3(i-1) ); Rx(i-2) = ( a(i-2) +b(i-2)+c(i-2) )*q(i-3,1); Ry(i-2) = ( a(i-2) +b(i-2)+c(i-2) )*q(i-3,2); Rz(i-2) = ( a(i-2) +b(i-2)+c(i-2) )*q(i-3,3); end %切矢 a(1)=0; b(1)=-3*W(2)/( W(1)* detal1(4) ); c(1)=3*W(2)/( W(1)* detal1(4) ); Rx(1) = 0; Ry(1) = 0; Rz(1) = 0; %切矢 a(m+3)=-3*W(m+K-1)/( W(m+K)* detal1(m+K) ); b(m+3)=3*W(m+K-1)/( W(m+K)* detal1(m+K) ); c(m+3)=0 ; Rx(m+3) = 0; Ry(m+3)= 0; Rz(m+3) = 0; % for i=2:m+K-1 % Rx(i) = rx(i-1 ) ; % Ry(i) = ry(i-1 ) ; % end A=zeros(m+3,m+3); A(1,1)=b(1); A(1,2)=c(1); A(m+3,m+2)=a(m+3); A(m+3,m+3)=b(m+3); for i=2:(m+2); A(i,i-1)=a(i); A(i,i)=b(i); A(i,i+1)=c(i); end Dx(1: m+K)= PivotGauss(A,Rx); Dy(1: m+K)= PivotGauss(A,Ry); Dz(1: m+K)= PivotGauss(A,Rz); %德步尔法求NURBS曲线 %------------插值并作出样条曲线----------------- x_boor=0;y_boor=0;down=0; for j=1:m uu=(U(j+3)):0.0005:U(j+4); for kk=1:length(uu) down=down+1; t1(down)= Base(j,3,U,uu(kk)); t2(down)= Base(j+1,3,U,uu(kk)); t3(down)= Base(j+2,3,U,uu(kk)); t4(down)= Base(j+3,3,U,uu(kk)); temp_x_up = ( Dx(j)*W(j)*Base(j,3,U,uu(kk)) + Dx(j+1)*W(j+1)*Base(j+1,3,U,uu(kk)) + Dx(j+2)*W(j+2)*Base(j+2,3,U,uu(kk)) + Dx(j+3)*W(j+3)*Base(j+3,3,U,uu(kk)) ); temp_x_down = W(j)*Base(j,3,U,uu(kk)) + W(j+1)*Base(j+1,3,U,uu(kk)) + W(j+2)*Base(j+2,3,U,uu(kk)) + W(j+3)*Base(j+3,3,U,uu(kk)) ; x_boor(down)=temp_x_up/temp_x_down ; y_boor(down)= ( Dy(j)*W(j)*Base(j,3,U,uu(kk)) + Dy(j+1)*W(j+1)*Base(j+1,3,U,uu(kk)) +