For fun: How many points does it take to define a sphere's radius?

[Patriot_1776]

Pat 1: How many points in 3D space does it take to define the radius?

Part 2:

a. If given the points, how would you model it?

b. What is the resulting radius?

c. What is the location of the radius from the default CS?

Have fun!

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[Patriot_1776]

Nobody wants to take a stab at this?

[Constantin]

ok, not sure if this is a trick question...

Part 1: (if we are talking of a "radius" as in circle segment) 3

Part 2:

a. plane through three points, sketcher, three point arc

b. depends on the given points

c. see b.

[DavidHerman]

Part 1: 4

(x - xo)^2 + (y - yo)^2 + (z - zo^2) = R^2

xo, yo, zo, and R are unknowns, so 4 points will give you 4 equations to solve for the 4 unknowns.

Part 2:

a. Center your sketch at xo, yo, zo; draw an arc of radius R; revolve.

b. R

c. Distance of center of sphere to default CS is sqrt(xo^2 + yo^2 + zo^2)

[Patriot_1776]

4 points it is. Good job! I can't vouch for the math, but I'll post my model shortly.

Before that, I'll list the points based off the default CS:

!

! DATUM POINT ARRAY DATA FILE

!

! Comment lines should begin with an exclamation mark (!).

! You may have as many comment lines as you wish.

! There must be at least one space between values.

!

! Enter values with respect to datum arrays' coordinate system:

!

!CARTESIAN coordinates:

! X Y Z

!

1.000 2.000 3.000

2.000 4.000 12.000

3.000 16.000 12.000

60.000 25.000 0.000

So, relative to the default CS, what's the radius, and where is it located in X, Y, and Z?

[DavidHerman · Accepted solution]

This is easier. No math involved. For 4 points, A,B,C,D.

1. Create a plane through 3 points, ABC

2. Sketch a circle through the three points A,B,C

3. Create an axis through the center of the circle

4. Create a plane through the axis and point D

5. Sketch a circle through point D and the intersection points of the circle and plane.

This sketch is the circumference of the sphere.

For the points you gave, the center is 32.93, 7.46, 3.02 and the radius is 32.39

[Patriot_1776]

Good job. I actually did it a little differently, but very close.

Funny, I realized I'd posted this before as "noname" when I first did it in '07. I recently ran across that thread again. Only you and Grahame did it.