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janhardo

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11 years, 7 days
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A procedure for quadric surfaces ...

janhardo 335 Maple
quadratic 3d plotting
July 16 2020
1 2

I am going now into 3D with the conics 
Ax^2+BY^2 +Cz^2 +Dxy'..........................................(general formula quadric surfaces)

Is there a existing procedure in Maple for this. 
Perhaps also with different coordinate systems ?
Probably is this too much asked.

I followed the post about two intersected cilinders.

 

  

Programming toolbox...

janhardo 335
programming toolbox
July 14 2020
1 13

Back in 2000 there was a Maple programming toolbox to buy 
Can't find it ?

Rewriting general formula ...

janhardo 335 Maple
spam simplification conic
July 13 2020
1 7

Some rewriting for a general equation , how to do ?


 

Transformation of eq 1 in wanted eq 2 form

A*x^2+B*x*y+C*y^2+D*x+E*y+F = 0 (general form 2)

After complete square for x and y and some rearrangment (general form 2) ,  i got this equation eq1  

 

 

> 

(A*(x + (B*y + D)/(2*A))^2 + C*(y + (B*x + E)/(2*C))^2)/(-C*y^2 - E*y - 2*F + (B*y + D)^2/(4*A) - A*x^2 - D*x + (B*x + E)^2/(4*C))=1;

(A*(x+(1/2)*(B*y+D)/A)^2+C*(y+(1/2)*(B*x+E)/C)^2)/(-C*y^2-E*y-2*F+(1/4)*(B*y+D)^2/A-A*x^2-D*x+(1/4)*(B*x+E)^2/C) = 1

 (1)
> 

eg1:= (-4*A^2*C*x^2 + (-4*y^2*C^2 + (-8*B*x*y - 4*D*x - 4*E*y)*C - (B*x + E)^2)*A - (B*y + D)^2*C)/(4*A^2*C*x^2 + (4*y^2*C^2 + (4*D*x + 4*E*y + 8*F)*C - (B*x + E)^2)*A - (B*y + D)^2*C) = 1;

(-4*A^2*C*x^2+(-4*y^2*C^2+(-8*B*x*y-4*D*x-4*E*y)*C-(B*x+E)^2)*A-(B*y+D)^2*C)/(4*A^2*C*x^2+(4*y^2*C^2+(4*D*x+4*E*y+8*F)*C-(B*x+E)^2)*A-(B*y+D)^2*C) = 1

 (2)
> 

 

(1) wanted form of eg1
"A x^2+B x y+C y^2+D x+E y+F=0*("general form 2))

for M ≠ 0

 

(x+(B*y+D)/(2*A))^2/X+  (y+(B*x+E)/(2*C))^2/Y = 1

 

Note : what X and Y could be ? :   M/A and M/B  ..

So it must be possible to transform eq1  in this form  above ?

> 

 

Some background info

If B= 0 in (general form 2) you get (general form 1)  

 

(2) In book for M ≠ 0 as example we get this form
 Ax^2+Cy^2+Dx+Ey+F = 0(general form 1 )

(x+C/(2*A))^2*A/M+  (y+D/(2*B))^2*B/M = 1

> 

 


 

Download vraag1-herleidingconics2.mw

 

 

Classification of conic sections...

janhardo 335
simplification conic
July 09 2020
0 11

I must do some formula manipulation
 

Classification of conic sections

> 

restart; with(student):
> 

A*x^2+B*y^2+C*x+D*y+E=0;

A*x^2+B*y^2+C*x+D*y+E = 0

 (1)
> 

f:= A*x^2+B*y^2+C*x+D*y+E;

A*x^2+B*y^2+C*x+D*y+E

 (2)
> 

completesquare(f, x);

A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y+E

 (3)
> 

f:= A*x^2+B*y^2+C*x+D*y+E;

A*x^2+B*y^2+C*x+D*y+E

 (4)
> 

ans:=Student[Precalculus][CompleteSquare]( (4), [y] );

B*(y+(1/2)*D/B)^2+A*x^2+C*x+E-(1/4)*D^2/B

 (5)
> 

ans1:=Student[Precalculus][CompleteSquare]( (4), [x] );

A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y+E

 (6)
> 

ans+ans1;

B*(y+(1/2)*D/B)^2+A*x^2+C*x+2*E-(1/4)*D^2/B+A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y

 (7)
> 

B*(y + D/(2*B))^2 + A*x^2 + C*x + 2*E - D^2/(4*B) + A*(x + C/(2*A))^2 - C^2/(4*A) + B*y^2 + D*y = 0;

B*(y+(1/2)*D/B)^2+A*x^2+C*x+2*E-(1/4)*D^2/B+A*(x+(1/2)*C/A)^2-(1/4)*C^2/A+B*y^2+D*y = 0

 (8)

Now i must  get this form A( )^2 +B( )^2 = M  

> 

 


 

Download vraag_herleiding_conic_sections_formule.mw

 

 

No gridlines options for plot3d...

janhardo 335 Maple
plot3d 3d gridlines
July 06 2020
0 4

I like to show a domain as a roster of gridlines
The plotbuilder has not this option gridlines , so i must program this ?

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