Arc

Published on February 2017 | Categories: Documents | Downloads: 48 | Comments: 0 | Views: 332
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% Draw an arc between two points
p1=[-2 -2 -3];
p2=[10 15 20];
% Circle x²+y²+z²=Constant
%=> z=sqrt(Constant-x²-y²-);
Center=((p2+p1))./2;
xc=Center(1);
yc=Center(2);
zc=Center(3);
% Radius
R=norm((p2-p1))/2;
%Min=min(min(p1,p2));
%Max=max(max(p1,p2));
%x=linspace(Min,Max,20);
%y=linspace(Min,Max,20);
x=linspace(p1(1),p2(1),200);
y=linspace(p1(2),p2(2),200);
z=zc+sqrt((R^2)-((x-xc).^2)-((y-yc).^2));
figure, plot3(x,y,z), grid on, hold on
plot3(p1(1),p1(2),p1(3),'*','MarkerSize',10),
plot3(p2(1),p2(2),p2(3),'*','MarkerSize',10),
hold on, plot3(xc,yc,zc,'*','MarkerSize',10)
-----------------------------------------------------------------% CCW arc from P1 to P2 with length L
% (reverse points for CW arc)
P1=[150,300]; P2=[500,600];
P=P2-P1;
[ThC,C]=cart2pol(P(1),P(2));
f=inline('2*L*sin(Th/2)-C*Th','Th','L','C');
options=optimset('Display','off');
for inc=50:100:950
L=C+inc;
Th=fzero(f,sqrt(24*(1-C/L)),options,L,C);
R=C/(2*sin(Th/2));
[x,y]=pol2cart(ThC+(pi-Th)/2,R);
CC=P1+[x,y];
P=P1-CC;
ThP1=cart2pol(P(1),P(2));
[x,y]=pol2cart(linspace(ThP1,ThP1+Th),R);
plot(x+CC(1),y+CC(2)); hold on
end
daspect([1,1,1]); grid; hold off
-------------------------------------------------------------------v = 0:.01:1;
[x,y]= meshgrid(v,v);
z = sin(4*x+5*y).*cos(7*(x-y))+exp(x+y);
mesh(x,y,z)

% pick two arbitrary points
P1 = [.2 .3];
P2 = [.6 .9];
% bulid a parametric curve
t = (0:.01:1)';
% a straight line between the points
L_1 = (1-t)*P1 + t*P2;
% plus a parabolic offset, as a function of the
% parameter C. Thus as C --> 0, the curve approaches
% a straight line.
C = .5;
N = (P1-P2)*[0 -1;1 0];
L_2 = L_1 + C*(t.*(1-t))*N;
% Interpolate the parabolic curve to get z(x,y)
z_path = interp2(x,y,z,L_2(:,1),L_2(:,2));
% and plot the parabolic path in the surface
hold on
plot3(L_2(:,1),L_2(:,2),z_path,'r-')
------------------------% y=x^2/4p
% p is focal distance from vertex
%(x,y) is any point on curve
x=linspace(-5,5,100); % 100 point on curve
p=5; %
y=(x.^2)/4*p;
plot(x,y);
hold on;
stem(0,p,'r')
---------------------% parabola equation y = a * x^2 + y0
x0 = 0; y0 = 0.1;
x1 = 10; y1 = 1;
a = (y1 - y0) / (x1 * x1)
%
%
x
y

because y is horizontal axis and x is vertical axis
draw like this:
= [-x1 : 0.1 : x1]'; % draw range of x
= a * x.^2 + y0; % equation of parabola

plot(y, x, 'r')
hold on
plot(-y, x, 'g')
hold off

% draw red parabola
% draw green parabola

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