Faculty of Engineering and Applied Science

ENGI 2422 Engineering Mathematics 2

2008 Winter

Examples 1.5.1 - 1.5.3
Quadric Surfaces

Below are images based on plots generated by Maple for the quadric surfaces in Examples 1.5.1 to 1.5.3 of the lecture notes:

Example 1.5.1:

2x = 3y² + 4z²
This quadric surface is an elliptic paraboloid, aligned along the x axis, with its vertex at the origin.
 


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Example 1.5.2:

z² = 1 + x²
This quadric surface is a hyperbolic cylinder, aligned along the y axis.
 


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Example 1.5.3:

x² – y² + z² + 1 = 0
This quadric surface is a hyperboloid of two sheets, aligned along the y axis, with its centre at the origin.
 


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The Maple worksheet commands that generated the initial images follow:

plot3d([6*s,2*sqrt(s)*cos(t),sqrt(s)*sqrt(3)*sin(t)],
s=-0.1..0.4, t=0..2*Pi,
axes=normal, scaling=constrained, orientation=[-45,60],
title=`Example 1.5.1\nElliptic paraboloid`);
 
plot3d({[sinh(t),s,cosh(t)],[sinh(t),s,-cosh(t)]},
s=-5..5, t=-2..2,
axes=normal, scaling=constrained, orientation=[-45,60],
title=`Example 1.5.2\nHyperbolic cylinder`);
 
plot3d({[sinh(s)*cos(t),cosh(s),sinh(s)*sin(t)],
[sinh(s)*cos(t),-cosh(s),sinh(s)*sin(t)]},
s=-1.5..1.5, t=0..2*Pi,
axes=normal, scaling=constrained, orientation=[-45,60],
title=`Example 1.5.3\nHyperboloid of 2 sheets`);


The Maple worksheet is available at this link.