 # How to get the center of the circle between two points of the circle?

I have 2 vertices and I want to make circle, that those 2 vertices are reference points of the circle.
I know that one of the vertices (right one on picture) is center of circle horisontally.
So I have to know where is center of the circle and after that I just use spin tool.
Do you have any fast and easy way to do it ?

My way is:
Select right one vertice and extrude it down as far you like
Select both reference(original) vertices
Cursor to selected
Spin: steps 4 (to get 90 degrees angle)
Pivot point to cursor
Select one new vertex and scale it over middle edge (which I made first)
Select 2 crossing edges
Edges X intersection (addon)
Intersection point is middle point of circle

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you need 3 points to define a circle!
in this case you can have an infinity of solutions!

happy bl

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There are an infinite number of circles whose circumferance passes through 2 points. You need to choose a radius first. Now it’s ALOT simpler if one of the points in exactly on the y axis, and the center of the circle will also lie on the y axis. Is one point on the y axis, and do you want the center to also lie on the y axis?

Otherwise you would need to use the point slope method. The center of the circle will lie on the line passing through the center of that line segment (edge) and perpendicular to it’s slope. That is unless someone can come up with a clever, blender solution.

A quick and dirty way is this (see lowest image)

1. select the first vert, snap cursor to selected. Object mode. Add a circle with many verts ~200.
2. Scale that circle, and note the scale.
3. Repeat with the 2nd vert, add a second circle.
4. Select the edge, and both circles, ctrl-J to join them. Edit mode.
5. Where they interesect is an approximate center.

Thank you Blenderallday. I got exactly same results with my method than yours, center point of the circle.
Yes, center line y-axis (like I said, its the right vertex).
RickyBlender: I did maybe explained wrong. Those 2 vertices are part of existing (imaginary) circle and somewhere must be center point (same distance from both vertices)

still you need 3 points and you provided only 2 points!
so there are an infinite numbers of solutions
cannot compute that!

unless you have a specific radius or a center then you can !

salut

1 Like that point has to be horisontally same place than right vertex.

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Here’s how I’d do it. http://screencast.com/t/E0GAsEWc

Intersection of the Y axis and the edge perpendicular to the centre of the starting edge

Richards video is the clever Blender way

Thank you Richard, very fast.
This is very common situation on my modelling (also from photos), I know/see middle of arch/circle and another part of that also and I have to make circle or half circle or quarter circle, based on those 2 points.

sorry here is example with only 2 points
unless you know where the center or another value (angle ) then you can define which circle

so if you have only P1 and P2 then which circle you choose and how?

thanks

Maybe Richard you want to elaborate on where that intersection tool is or addon. Unless it’s a secret.

@[URL="/u/Photox
with your 2 circles example
you find the center of the segment but does not give you a specific circle for that segment!
still an interesting way to find the center of a segment!

happy bl

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Ricky. It gives you the center of a circle, not the center of the line segment. Center of circle, plus radius (or single point on circumfrance) gives you a circle. My point was that the line perpedicular to the segment and passing through it’s mid point will be the line that all circle centers must satisfy. Or something like that.

If you made a line between where the two circles intersect, that will intersect the line segment at it’s mid point. My head hurts. Bottom line: Richard’s tinycad solution is pretty the much the bomb here.

I know it’s the same thing, RickyBlender, but your diagram might be more convincing if you rotated the points so P2 was on the circle’s vertical radius, thus visually matching TynkaTopi’s original set up.

@TynkaTopi: Ricky is correct. The methods given can find A circle containing those two points, but not THE circle containing those points. When you ask geometrical questions, precise language is very important. Your question:

How to get the center of the circle between two points of the circle ?
says to a mathmetician that there is a unique circle that fits the requirements, otherwise it would ask: “how to get a center of some circle” which means you want a circle going through the points, but don’t particularly care which one.

Your second bit of information

I know that one of the vertices (right one on picture) is center of circle horisontally.

may have led you to believe you had more information than just two points, and so a unique solution would be possible, but, in fact, since circles are symetrical, that statement can be true about ANY point on a circle – it just depends on your point of view. So you really don’t know any more than the location of two points on the circumference. It is a geometrical fact that there are an infinite number of circles with the same two points on their circumference. To find a unique circle, you need another point.

True. Next time I dont use google translator (I wanted to be exact) And matter of fact we had more information, that x place of center point, my question was based on that fact.
Its common situation that you can see top of arch (center of x direction), and some other points.

I understand the second sentence in the original thread to mean that X position of the centre of the circle is known (the same as that for the right vertex). If that is the case then there is just one solution

Nice, you went through all directions your english is a lot better then mine
and it is very possible that the question was not very clear in terms of math!
but your explanations are very good and i thank you for giving a better math description

for me 2 points cannot give one specific circle!
unless some other point was not given !

thank you
happy bl

Here’s another, using trigonometry.

From top left:

• Because it is only know that there is two vertices sharing an edge, and that the other vertex is on the horizontal line (Z axis) where the center point is, length for that edge needs to be calculated. Using the global coordinates that is shown in the properties panel when selected, applying the position information and solve the length using shown formula
• Next for the angle that the known edge and horizontal line form: one edge is already known, and another is the absolute value of the other vertex global X axis position. Sine function is used to calculate the angle.
• Now there is angle and two edges known, using cosine function to solve for C, which is the radius
• Could also solve for h using pythagoras’ theorem, if needed
• Blender agrees with the calculation results.

To me the English is perfectly clear and gives more infomation than just the position of two points on the circle