bezier surface plotter question

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mohammad azsad
mohammad azsad 2014-11-20
评论： Dominik Cech 2021-8-27
i want to write program of bezier surface but it is wrong please help me this program that i wrote:
x=[12 23 13 4 5]';y=[12 4 15 23 7]';z=[1 14 25 2 7]'; p=[x,y,z];
bez = [];
n = size(p, 1) - 1;
O = 1; for v = 0:0.01:1; for u = 0:0.01:1;
suma = [0 0 0];
for i=0:n
for j=0:n
if i==0, res = 1;
elseif n==0, res = 0;
else
res = 1;
for a=1:i
res = res*((n - i + a)/a);
end
end
if j==0, res1 = 1;
elseif n==0, res1 = 0;
else
res1 = 1;
for a1=1:j
res1 = res1*((n - j + a1)/a1);
end
end
suma = suma + p(i+1, :)*res*(u^i)*((1 - u)^(n - i))*res1*(v^j)*((1 - v)^(n - j)) ;
end
bez(O, :) = suma;
O=O+1
end
end end
plot3(x,y,z,'k') hold on grid on
if ischar(fig) symbol = fig; elseif n < 30 symbol = 'o'; else symbol = '.';
end
for j = 1:n hPoints = plot3(p(:,1), p(:,2),p(:,3), symbol); hold on; end hold on, hbc = plot3(bez(:, 1), bez(:, 2), bez(:, 3), 'LineWidth', 3, 'Color', 'b'); % plots the Bezier curve legend([hbc], {'Bezier curve'}) title(sprintf('number of points: %d', n+1))
and the formula is
where is p is control points
and

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回答（1 个）

amina lk
amina lk 2014-12-2
this control point of curve ,you have to use 16 control point for you to draw a bezier surface
look this exemple of bezier surf
clear; clf; % Blending Function % Parametric Values u= 0 : 0.05 : 1; for i=1:21 U(i,1)=u(i)^3; U(i,2)=u(i)^2; U(i,3)=u(i); U(i,4)=1; end w= 0 : 0.05 : 1; for i=1:21 W(i,1)=w(i)^3; W(i,2)=w(i)^2; W(i,3)=w(i); W(i,4)=1; end % Cubic Bezier transformation Matrix M=[ -1 3 -3 1; 3 -6 3 0; -3 3 0 0; 1 0 0 0;]; % Control Vertices of patch1 % P00 p10 p20 p30 p01 p11 p21 p31 p02 p12 p22 p32 p03 p13 p23 p33 patch1 = [-5, -2, 2, 5, -4, -2.5, 2.5, 4, -8.5, -4.5, 4.5, 8.5, -7, -3, 3, 7; 1, 3, 3, 1, 1, 2, 2, 1, -1, 0, 0, -1, 2, 4, 4, 2; -6, -6, -6, -6, -3, -3, -3, -3, 1, 3, 3, 1, 5, 6.5, 6.5, 5; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; % Control Vertices of patch1 CV_X=[ patch1(1,1) patch1(1,5) patch1(1,9) patch1(1,13); patch1(1,2) patch1(1,6) patch1(1,10) patch1(1,14); patch1(1,3) patch1(1,7) patch1(1,11) patch1(1,15); patch1(1,4) patch1(1,8) patch1(1,12) patch1(1,16);]; CV_Y=[ patch1(2,1) patch1(2,5) patch1(2,9) patch1(2,13); patch1(2,2) patch1(2,6) patch1(2,10) patch1(2,14); patch1(2,3) patch1(2,7) patch1(2,11) patch1(2,15); patch1(2,4) patch1(2,8) patch1(2,12) patch1(2,16);]; CV_Z=[ patch1(3,1) patch1(3,5) patch1(3,9) patch1(3,13); patch1(3,2) patch1(3,6) patch1(3,10) patch1(3,14); patch1(3,3) patch1(3,7) patch1(3,11) patch1(3,15); patch1(3,4) patch1(3,8) patch1(3,12) patch1(3,16);]; % Bezier Surfaces for i=1:21 for j=1:21 P_X(i,j)=U(i,:)*M*CV_X*M'*W(j,:)'; P_Y(i,j)=U(i,:)*M*CV_Y*M'*W(j,:)'; P_Z(i,j)=U(i,:)*M*CV_Z*M'*W(j,:)'; end end % figure lange MIN_X=-8; MAX_X=8; MIN_Y=-8; MAX_Y=8; MIN_Z=-8; MAX_Z=8; %Plot Bezier Surfaces figure(1); axis ([MIN_X, MAX_X, MIN_Y, MAX_Y, MIN_Z, MAX_Z]); title('4-1 : Bezier Surfaces (SCREW ANGLE)'); xlabel('X'); ylabel('Y'); Zlabel('Z'); hold on; for i=1:21 plot3 (P_X(:,i), P_Y(:,i), P_Z(:,i), 'k'); plot3 (P_X(i,:), P_Y(i,:), P_Z(i,:), 'k'); end for i=1:4 plot3 (CV_X(:,i), CV_Y(:,i), CV_Z(:,i), ':'); plot3 (CV_X(i,:), CV_Y(i,:), CV_Z(i,:), ':'); end hold off; figure(2); axis ([MIN_X, MAX_X, MIN_Z, MAX_Z]); title('4-1 : Bezier Surfaces (SIDE VIEW1)'); xlabel('X'); ylabel('Z'); hold on; for i=1:21 plot (P_X(:,i), P_Z(:,i), 'k'); plot (P_X(i,:), P_Z(i,:), 'k'); end for i=1:4 plot (CV_X(:,i), CV_Z(:,i), ':'); plot (CV_X(i,:), CV_Z(i,:), ':'); end hold off; figure(3); axis ([MIN_Y, MAX_Y, MIN_Z, MAX_Z]); title('4-1 : Bezier Surfaces (SIDE VIEW2)'); xlabel('Y'); ylabel('Z'); hold on; for i=1:21 plot (P_Y(:,i), P_Z(:,i), 'k'); plot (P_Y(i,:), P_Z(i,:), 'k'); end for i=1:4 plot (CV_Y(:,i), CV_Z(:,i), ':'); plot (CV_Y(i,:), CV_Z(i,:), ':'); end hold off figure(4); axis ([MIN_X, MAX_X, MIN_Y, MAX_Y]); title('4-1 : Bezier Surfaces (TOP VIEW)'); xlabel('X'); ylabel('Y'); hold on; for i=1:21 plot (P_X(:,i), P_Y(:,i), 'k'); plot (P_X(i,:), P_Y(i,:), 'k'); end for i=1:4 plot (CV_X(:,i), CV_Y(:,i), ':'); plot (CV_X(i,:), CV_Y(i,:), ':'); end hold off

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