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geom3d

  

RadicalPlane

  

find the radical plane of two given spheres

  

RadicalLine

  

find the radical line of three given spheres

  

RadicalCenter

  

find the radical center of four given spheres

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RadicalPlane(p1, s1, s2)

RadicalLine(p1, s1, s2, s3)

RadicalCenter(p1, s1, s2, s3, s4)

Parameters

p

-

name

s1, s2, s3, s4

-

spheres

Description

• 

The locus of points Px,y,z which have the same power with respect to the two given spheres s1, s2 is a plane called radical plane.

• 

Let us introduce a third sphere s3. Now we have three radical planes that form a pencil whose axis is the straight line. This line is called the radical line of the three sphere.

• 

Now add a fourth sphere s4, and we have four radical lines. These four lines are clearly concurrent at the radical center.

Examples

withgeom3d:

Define two spheres s1, s2

spheres1,x2+y2+z2=1,x,y,z:

spheres2,pointB,5,5,5,2:

Find the radical plane of s1 and s2

RadicalPlanep,s1,s2

p

(1)

Equationp

72+10x+10y+10z=0

(2)

NormalVectorp

10,10,10

(3)

Simple check:

Generate a randpoint point on the radical plane:

randpointP,p

P

(4)

The power of point P with respect to two spheres s1 and s2 must be the same:

powerpsP,s1powerpsP,s2

0

(5)

Plotting:

drawp,s1,s2,style=patchnogrid,orientation=26,96,lightmodel=light1,title=`Radical plane of two given spheres`

Find the radical line of three spheres:

spheres3,pointA,1,2,3,3

s3

(6)

RadicalLinel,s1,s2,s3

l

(7)

detaill

Warning, assume that the parameter in the parametric equations is _t

name of the objectlform of the objectline3dequation of the linex=575+20_t,y=21540_t,z=20_t

(8)

Find the radical center of four given spheres:

spheres4,pointA,3,7,1,3

s4

(9)

RadicalCenterP,s1,s2,s3,s4

P

(10)

formP

point3d

(11)

coordinatesP

249100,471100,0

(12)

See Also

geom3d[sphere]

 


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