![[Maple Plot]](images/Quadric Surface1.gif)
QUADRIC SURFACES
Cone
| > | restart: |
| > | with(plots): |
Warning, the name changecoords has been redefined
| > | R:=(r,t)->[3*r*cos(t),2*r*sin(t),r]: |
| > | R1:=(r,t)->[3*r*cos(t),2*r*sin(t),-r]: |
| > |
| > | f:=proc(t) spacecurve(R(s,t),s=0..1,thickness=2): end: |
| > | g:=proc(t) spacecurve(R1(s,t),s=0..1,thickness=2): end: |
| > | h:=proc(s) spacecurve(R(s,t),t=0..2*Pi,thickness=2): end: k:=proc(s) spacecurve(R1(s,t),t=0..2*Pi,thickness=2):end: |
| > | display(seq( display(seq([f(a),g(a),h(a/8),k(a/8)],a=-8..N)) ,N=-8..8),insequence=true,axes=framed,labels=[X,Y,Z]); |
| > |
| > |
| > |
| > |
Elliptic Paraboloid
| > | with(plots): |
| > | r:=(s,t)->[s*cos(t),s*sin(t),s^2]: |
| > | f:=proc(s) spacecurve(r(s,t),t=0..2*Pi,thickness=2): end: |
| > | g:=proc(t) spacecurve(r(s,t),s=-6..6,thickness=2): end: |
| > | display(seq( display(seq([g(a/2),f(a/2)],a=-12..N)) ,N=-12..12),insequence=true,axes=framed,labels=[X,Y,Z]); |
![[Maple Plot]](images/Quadric Surface2.gif)
Ellipsoid
| > | restart: |
| > | with(plots): |
Warning, the name changecoords has been redefined
| > | R:=(r,t)->[3*r*cos(t),2*r*sin(t),sqrt(1-r^2)]: |
| > | R1:=(r,t)->[3*r*cos(t),2*r*sin(t),-sqrt(1-r^2)]: |
| > |
| > | f:=proc(t) spacecurve(R(s,t),s=-1..1,thickness=2): end: |
| > | g:=proc(t) spacecurve(R1(s,t),s=-1..1,thickness=2): end: |
| > | h:=proc(s) spacecurve(R(s,t),t=0..2*Pi,thickness=2): end: k:=proc(s) spacecurve(R1(s,t),t=0..2*Pi,thickness=2):end: |
| > | display(seq( display(seq([f(a),g(a),h(a/20),k(a/20)],a=-20..N)) ,N=-20..20),insequence=true,axes=framed,labels=[X,Y,Z],tickmarks=[3,3,3]); |
![[Maple Plot]](images/Quadric Surface3.gif)
| > |
Hyperbolic Paraboloid
| > | restart: |
| > | with(plots): |
Warning, the name changecoords has been redefined
| > | R:=(r,t)->[3*r*cos(t),2*r*sin(t),r^2*cos(2*t)]: |
| > |
| > | f:=proc(t) spacecurve(R(s,t),s=0..10,color=COLOR(HUE,0.89),thickness=2): end: |
| > |
| > | g:=proc(s) spacecurve(R(s,t),t=0..2*Pi,color=cyan,thickness=2): end: |
| > |
| > | display(seq( display(seq([g(a/2.4),f(a)],a=-24..N)) ,N=-24..24),insequence=true,axes=framed,labels=[X,Y,Z],tickmarks=[3,3,3]); |
![[Maple Plot]](images/Quadric Surface4.gif)
| > |
Hyperboloid of One Sheet
| > | restart: |
| > | with(plots): |
Warning, the name changecoords has been redefined
| > | R:=(r,t)->[3*r*cos(t),2*r*sin(t),sqrt(r^2-1)]: |
| > | R1:=(r,t)->[3*r*cos(t),2*r*sin(t),-sqrt(r^2-1)]: |
| > | f:=proc(t) spacecurve(R(s,t),s=1..4,thickness=2): end: |
| > |
| > | g:=proc(s) spacecurve(R(s,t),t=0..2*Pi,thickness=2): end: |
| > | h:=proc(t) spacecurve(R1(s,t),s=1..4,thickness=2): end: |
| > | k:=proc(s) spacecurve(R1(s,t),t=0..2*Pi,thickness=2): end: |
| > | display(seq( display(seq([g(a/2),f(a),h(a),k(a/2)],a=-8..N)) ,N=-8..8),insequence=true,axes=framed,tickmarks=[3,3,3],labels=[X,Y,Z]); |
![[Maple Plot]](images/Quadric Surface5.gif)
| > |
| > |
Hyperboloid of Two Sheet
| > | restart: |
| > | with(plots): |
Warning, the name changecoords has been redefined
| > | R:=(r,t)->[3*r*cos(t),2*r*sin(t),sqrt(r^2+1)]: |
| > | R1:=(r,t)->[3*r*cos(t),2*r*sin(t),-sqrt(r^2+1)]: |
| > | f:=proc(t) spacecurve(R(s,t),s=1..4,thickness=2): end: |
| > |
| > | g:=proc(s) spacecurve(R(s,t),t=0..2*Pi,thickness=2): end: |
| > | h:=proc(t) spacecurve(R1(s,t),s=1..4,thickness=2): end: |
| > | k:=proc(s) spacecurve(R1(s,t),t=0..2*Pi,thickness=2): end: |
| > | display(seq( display(seq([g(a/2),f(a),h(a),k(a/2)],a=-8..N)) ,N=-8..8),insequence=true,axes=framed,tickmarks=[3,3,3],labels=[X,Y,Z]); |
![[Maple Plot]](images/Quadric Surface6.gif)
| > |
| > |
| > |