改进后的坐标变换的matlab代码，本次发一个例子，另外三个原理类似。 close all; clear; clc; %3.11动画演示 % 坐标系（Xi,Yi,Zi） % 绕Z轴旋转30°R（Z，30）得（X1,Y1,Z1） % 绕Y1轴旋转45°R（Y1,45）得（X2,Y2,Z2） %再绕Z2轴旋转60°R（Z2,60）得（Xj,Yj,Zj） x0 = 0:3:50;%建立原始三维坐标x轴 y0 = zeros(1,length(x0)); z0 = zeros(1,length(x0));%建立原始三维坐标x轴 X1 = zeros(1,length(x0));%建立原始三维坐标y轴 y1 = 0:3:50; z1 = zeros(1,length(x0));%建立原始三维坐标y轴 x2 = zeros(1,length(x0));%建立原始三维坐标z轴 y2 = zeros(1,length(x0)); z2 = 0:3:50;%建立原始三维坐标z轴 u0 = 45:5/(length(x0)-1):50; v0 = 50 – u0; w0 = zeros(1,length(x0)); l0 = 45:5/(length(x0)-1):50; j0 = -50+u0; k0 = zeros(1,length(x0)); u1 = 0:5/(length(x0)-1):5; v1 = 50 – u1; w1 = zeros(1,length(x0)); l1 = -5:5/(length(x0)-1):0; j1 = 50+l1; k1 = zeros(1,length(x0)); u2 = zeros(1,length(x0)); v2 = 0:5/(length(x0)-1):5; w2 = 50-v2; l2 = zeros(1,length(x0)); j2 = -5:5/(length(x0)-1):0; k2 = 50+j2; t1 = 0:pi/(6*(length(x0)-1)):pi/6; for i1 = 1:length(x0) T1 = [cos(t1(i1)) -sin(t1(i1)) 0;sin(t1(i1)) cos(t1(i1)) 0;0 0 1];%旋转矩阵(绕Z轴旋转) % T2 = [1 0 0;0 cos(t1(i1)) -sin(t1(i1));0 sin(t1(i1)) cos(t1(i1))];%旋转矩阵（绕X轴旋转） B = T1*[x0;y0;z0]; B1 = T1*[u0;v0;w0]; B2 = T1*[l0;j0;k0]; x3 = zeros(1,length(x0)); y3 = zeros(1,length(x0)); z3 = zeros(1,length(x0)); u3 = zeros(1,length(x0)); v3 = zeros(1,length(x0)); w3 = zeros(1,length(x0)); l3 = zeros(1,length(x0)); j3 = zeros(1,length(x0)); k3 = zeros(1,length(x0)); for i = 1:length(x0) x3(i) = B(1,i); y3(i) = B(2,i); z3(i) = B(3,i); u3(i) = B1(1,i); v3(i) = B1(2,i); w3(i) = B1(3,i); l3(i) = B2(1,i); j3(i) = B2(2,i); k3(i) = B2(3,i); end C = T1*[X1;y1;z1]; C1 = T1*[u1;v1;w1]; C2 = T1*[l1;j1;k1]; x4 = zeros(1,length(x0)); y4 = zeros(1,length(x0)); z4 = zeros(1,length(x0)); u4 = zeros(1,length(x0)); v4 = zeros(1,length(x0)); w4 = zeros(1,length(x0)); l4 = zeros(1,length(x0)); j4 = zeros(1,length(x0)); k4 = zeros(1,length(x0)); for i = 1:length(x0) x4(i) = C(1,i); y4(i) = C(2,i); z4(i) = C(3,i); u4(i) = C1(1,i); v4(i) = C1(2,i); w4(i) = C1(3,i); l4(i) = C2(1,i); j4(i) = C2(2,i); k4(i) = C2(3,i); end D = T1*[x2;y2;z2]; D1 = T1*[u2;v2;w2]; D2 = T1*[l2;j2;k2]; x5 = zeros(1,length(x0)); y5 = zeros(1,length(x0)); z5 = zeros(1,length(x0)); u5 = zeros(1,length(x0)); v5 = zeros(1,length(x0)); w5 = zeros(1,length(x0)); l5 = zeros(1,length(x0)); j5 = zeros(1,length(x0)); k5 = zeros(1,length(x0)); for i = 1:length(x0) x5(i) = D(1,i); y5(i) = D(2,i); z5(i) = D(3,i); u5(i) = D1(1,i); v5(i) = D1(2,i); w5(i) = D1(3,i); l5(i) = D2(1,i); j5(i) = D2(2,i); k5(i) = D2(3,i); end plot3(x0,y0,z0,’b’); hold on; plot3(u0,v0,w0,’b’); plot3(l0,j0,k0,’b’); text(x0(length(x0))+5,y0(length(x0))+5,z0(length(x0))+5,’Xi轴’); text(x0(1),y0(1),z0(1),'(Oi,O1,O2,Oj)’); plot3(X1,y1,z1,’b’); text(X1(length(x0))+5,y1(length(x0))+5,z1(length(x0))+5,’Yi轴’); plot3(u1,v1,w1,’b’); plot3(l1,j1,k1,’b’); plot3(x2,y2,z2,’b’); plot3(u2,v2,w2,’b’); plot3(l2,j2,k2,’b’); text(x2(length(x0))+5,y2(length(x0))+5,z2(length(x0))+5,’Zi轴’); plot3(x3,y3,z3,’r’); plot3(u3,v3,w3,’r’); plot3(l3,j3,k3,’r’); text(x3(length(x0))+5,y3(length(x0))+5,z3(length(x0))+5,’X1轴’); plot3(x4,y4,z4,’r’); plot3(u4,v4,w4,’r’); plot3(l4,j4,k4,’r’); text(x4(length(x0))+5,y4(length(x0))+5,z4(length(x0))+5,’Y1轴’); plot3(x5,y5,z5,’r’); plot3(u5,v5,w5,’r’); plot3(l5,j5,k5,’r’); text(x5(length(x0))+5,y5(length(x0))+5,z5(length(x0))+5,’Z1轴’); xlabel(‘X轴’); ylabel(‘Y轴’); zlabel(‘Z轴’); aXis equal; aXis([-50 50 -50 50 -50 50]); getframe; hold off; end t1 = 0:pi/(4*(length(x0)-1)):pi/4; for i1 = 1:length(x0) T2 = [cos(t1(i1)) 0 -sin(t1(i1));0 1 0;sin(t1(i1)) 0 cos(t1(i1))]; E = T1*T2*[x0;y0;z0]; E1 = T1*T2*[u0;v0;w0]; E2 = T1*T2*[l0;j0;k0]; x6 = zeros(1,length(x0)); y6 = zeros(1,length(x0)); z6 = zeros(1,length(x0)); u6 = zeros(1,length(x0)); v6 = zeros(1,length(x0)); w6 = zeros(1,length(x0)); l6 = zeros(1,length(x0)); j6 = zeros(1,length(x0)); k6 = zeros(1,length(x0)); for i = 1:length(x0) x6(i) = E(1,i); y6(i) = E(2,i); z6(i) = E(3,i); u6(i) = E1(1,i); v6(i) = E1(2,i); w6(i) = E1(3,i); l6(i) = E2(1,i); j6(i) = E2(2,i); k6(i) = E2(3,i); end F = T1*T2*[X1;y1;z1]; F1 = T1*T2*[u1;v1;w1]; F2 = T1*T2*[l1;j1;k1]; x7 = zeros(1,length(x0)); y7 = zeros(1,length(x0)); z7 = zeros(1,length(x0)); u7 = zeros(1,length(x0)); v7 = zeros(1,length(x0)); w7 = zeros(1,length(x0)); l7 = zeros(1,length(x0)); j7 = zeros(1,length(x0)); k7 = zeros(1,length(x0)); for i = 1:length(x0) x7(i) = F(1,i); y7(i) = F(2,i); z7(i) = F(3,i); u7(i) = F1(1,i); v7(i) = F1(2,i); w7(i) = F1(3,i); l7(i) = F2(1,i); j7(i) = F2(2,i); k7(i) = F2(3,i); end G = T1*T2*[x2;y2;z2]; G1 = T1*T2*[u2;v2;w2]; G2 = T1*T2*[l2;j2;k2]; x8 = zeros(1,length(x0)); y8 = zeros(1,length(x0)); z8 = zeros(1,length(x0)); u8 = zeros(1,length(x0)); v8 = zeros(1,length(x0)); w8 = zeros(1,length(x0)); l8 = zeros(1,length(x0)); j8 = zeros(1,length(x0)); k8 = zeros(1,length(x0)); for i = 1:length(x0) x8(i) = G(1,i); y8(i) = G(2,i); z8(i) = G(3,i); u8(i) = G1(1,i); v8(i) = G1(2,i); w8(i) = G1(3,i); l8(i) = G2(1,i); j8(i) = G2(2,i); k8(i) = G2(3,i); end plot3(x0,y0,z0,’b’); hold on; plot3(u0,v0,w0,’b’); plot3(l0,j0,k0,’b’); text(x0(length(x0))+5,y0(length(x0))+5,z0(length(x0))+5,’Xi轴’); text(x0(1),y0(1),z0(1),'(Oi,O1,O2,Oj)’); plot3(X1,y1,z1,’b’); plot3(u1,v1,w1,’b’); plot3(l1,j1,k1,’b’); text(X1(length(x0))+5,y1(length(x0))+5,z1(length(x0))+5,’Yi轴’); plot3(x2,y2,z2,’b’); plot3(u2,v2,w2,’b’); plot3(l2,j2,k2,’b’); text(x2(length(x0))+5,y2(length(x0))+5,z2(length(x0))+5,’Zi轴’); plot3(x3,y3,z3,’r’); plot3(u3,v3,w3,’r’); plot3(l3,j3,k3,’r’); text(x3(length(x0))+5,y3(length(x0))+5,z3(length(x0))+5,’X1轴’); plot3(x4,y4,z4,’r’); plot3(u4,v4,w4,’r’); plot3(l4,j4,k4,’r’); text(x4(length(x0))+5,y4(length(x0))+5,z4(length(x0))+5,’Y1轴’); plot3(x5,y5,z5,’r’); plot3(u5,v5,w5,’r’); plot3(l5,j5,k5,’r’); text(x5(length(x0))+5,y5(length(x0))+5,z5(length(x0))+5,’Z1轴’); plot3(x6,y6,z6,’k’); plot3(u6,v6,w6,’k’); plot3(l6,j6,k6,’k’); text(x6(length(x0))+5,y6(length(x0))+5,z6(length(x0))+5,’X2轴’); plot3(x7,y7,z7,’k’); plot3(u7,v7,w7,’k’); plot3(l7,j7,k7,’k’); text(x7(length(x0))+5,y7(length(x0))+5,z7(length(x0))+5,’Y2轴’); plot3(x8,y8,z8,’k’); plot3(u8,v8,w8,’k’); plot3(l8,j8,k8,’k’); text(x8(length(x0))+5,y8(length(x0))+5,z8(length(x0))+5,’Z2轴’); xlabel(‘X轴’); ylabel(‘Y轴’); zlabel(‘Z轴’); aXis equal; aXis([-50 50 -50 50 -50 50]); getframe; hold off; end t1 = 0:pi/(3*(length(x0)-1)):pi/3; for i1 = 1:length(x0) T3 = [cos(t1(i1)) -sin(t1(i1)) 0;sin(t1(i1)) cos(t1(i1)) 0;0 0 1];%旋转矩阵(绕Z轴旋转) E = T1*T2*T3*[x0;y0;z0]; E1 = T1*T2*T3*[u0;v0;w0]; E2 = T1*T2*T3*[l0;j0;k0]; x9 = zeros(1,length(x0)); y9 = zeros(1,length(x0)); z9 = zeros(1,length(x0)); u9 = zeros(1,length(x0)); v9 = zeros(1,length(x0)); w9 = zeros(1,length(x0)); l9 = zeros(1,length(x0)); j9 = zeros(1,length(x0)); k9 = zeros(1,length(x0)); for i = 1:length(x0) x9(i) = E(1,i); y9(i) = E(2,i); z9(i) = E(3,i); u9(i) = E1(1,i); v9(i) = E1(2,i); w9(i) = E1(3,i); l9(i) = E2(1,i); j9(i) = E2(2,i); k9(i) = E2(3,i); end F = T1*T2*T3*[X1;y1;z1]; F1 = T1*T2*T3*[u1;v1;w1]; F2 = T1*T2*T3*[l1;j1;k1]; X10 = zeros(1,length(x0)); y10 = zeros(1,length(x0)); z10 = zeros(1,length(x0)); u10 = zeros(1,length(x0)); v10 = zeros(1,length(x0)); w10 = zeros(1,length(x0)); l10 = zeros(1,length(x0)); j10 = zeros(1,length(x0)); k10 = zeros(1,length(x0)); for i = 1:length(x0) X10(i) = F(1,i); y10(i) = F(2,i); z10(i) = F(3,i); u10(i) = F1(1,i); v10(i) = F1(2,i); w10(i) = F1(3,i); l10(i) = F2(1,i); j10(i) = F2(2,i); k10(i) = F2(3,i); end G = T1*T2*T3*[x2;y2;z2]; G1 = T1*T2*T3*[u2;v2;w2]; G2 = T1*T2*T3*[l2;j2;k2]; X11 = zeros(1,length(x0)); y11 = zeros(1,length(x0)); z11 = zeros(1,length(x0)); u11 = zeros(1,length(x0)); v11 = zeros(1,length(x0)); w11 = zeros(1,length(x0)); l11 = zeros(1,length(x0)); j11 = zeros(1,length(x0)); k11 = zeros(1,length(x0)); for i = 1:length(x0) X11(i) = G(1,i); y11(i) = G(2,i); z11(i) = G(3,i); u11(i) = G1(1,i); v11(i) = G1(2,i); w11(i) = G1(3,i); l11(i) = G2(1,i); j11(i) = G2(2,i); k11(i) = G2(3,i); end plot3(x0,y0,z0,’b’); hold on; plot3(u0,v0,w0,’b’); plot3(l0,j0,k0,’b’); text(x0(length(x0))+5,y0(length(x0))+5,z0(length(x0))+5,’Xi轴’); text(x0(1),y0(1),z0(1),'(Oi,O1,O2,Oj)’); plot3(X1,y1,z1,’b’); plot3(u1,v1,w1,’b’); plot3(l1,j1,k1,’b’); text(X1(length(x0))+5,y1(length(x0))+5,z1(length(x0))+5,’Yi轴’); plot3(x2,y2,z2,’b’); plot3(u2,v2,w2,’b’); plot3(l2,j2,k2,’b’); text(x2(length(x0))+5,y2(length(x0))+5,z2(length(x0))+5,’Zi轴’); plot3(x3,y3,z3,’r’); plot3(u3,v3,w3,’r’); plot3(l3,j3,k3,’r’); text(x3(length(x0))+5,y3(length(x0))+5,z3(length(x0))+5,’X1轴’); plot3(x4,y4,z4,’r’); plot3(u4,v4,w4,’r’); plot3(l4,j4,k4,’r’); text(x4(length(x0))+5,y4(length(x0))+5,z4(length(x0))+5,’Y1轴’); plot3(x5,y5,z5,’r’); plot3(u5,v5,w5,’r’); plot3(l5,j5,k5,’r’); text(x5(length(x0))+5,y5(length(x0))+5,z5(length(x0))+5,’Z1轴’); plot3(x6,y6,z6,’k’); plot3(u6,v6,w6,’k’); plot3(l6,j6,k6,’k’); text(x6(length(x0))+5,y6(length(x0))+5,z6(length(x0))+5,’X2轴’); plot3(x7,y7,z7,’k’); plot3(u7,v7,w7,’k’); plot3(l7,j7,k7,’k’); text(x7(length(x0))+5,y7(length(x0))+5,z7(length(x0))+5,’Y2轴’); plot3(x8,y8,z8,’k’); plot3(u8,v8,w8,’k’); plot3(l8,j8,k8,’k’); text(x8(length(x0))+5,y8(length(x0))+5,z8(length(x0))+5,’Z2轴’); plot3(x9,y9,z9,’g’); plot3(u9,v9,w9,’g’); plot3(l9,j9,k9,’g’); text(x9(length(x0))+5,y9(length(x0))+5,z9(length(x0))+5,’Xj轴’); plot3(X10,y10,z10,’g’); plot3(u10,v10,w10,’g’); plot3(l10,j10,k10,’g’); text(X10(length(x0))+5,y10(length(x0))+5,z10(length(x0))+5,’Yj轴’); plot3(X11,y11,z11,’g’); plot3(u11,v11,w11,’g’); plot3(l11,j11,k11,’g’); text(X11(length(x0))+5,y11(length(x0))+5,z11(length(x0))+5,’Zj轴’); xlabel(‘X轴’); ylabel(‘Y轴’); zlabel(‘Z轴’); aXis equal; aXis([-50 50 -50 50 -50 50]); getframe; hold off; end
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