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Formula for 3D plot of a circle

This project relates to 3D graphics. ? I need the mathematical formula for the 3D plot of a circle. ? The circle can be centred at any point, on any plane; ? and the camera can be at any point in any orientation. ? ?

I need the formula in terms that I understand, using my presentation of the problem, so I'll give you my 3D projection of (x,y,z) formula and I'll expect the answer in terms of these variable names.

## Deliverables

Here I'm using capitals for 3D vectors and lowercase for scalars. ? In our interaction, I don't want to use any fancy non-keyboard symbols.

The circle:

_________

K = circle centre

g = circle radius

N = face normal for the plane the circle is on

P = unknown point which is on the circle

The equations of the circle are:

(P - K) . (P - K) = g^2

(P - K) x N = 0

I'm using this formula for the 3D plot of a point:

______________________________________

C = camera position

D = camera forward direction

U = camera up direction

R = camera right direction

P = arbitrary point

(centre_x, centre_y) = point in the centre of the image, in pixels

scale_x, scale_y = scalars to transform the?

(x,y) = projection of the point into the image, in pixels

Let W = P - C

d = Wx*Dx + Wy*Dy + Wz*Dz

u = Wx*Ux + Wy*Uy + Wz*Uz

r = Wx*Rx + Wy*Ry + Wz*Rz

x = r*scale_x/d + centre_x

y = u*scale_y/d + centre_y

My apologies if my symbology is non-standard.

What I want is an equation with 2 unknowns: ? 'x' and 'y', defining the curve that the circle (above) makes when projected onto a 2D surface using the given formula (below).

Habilidades: Engenharia, MySQL, PHP, Arquitetura de software, Teste de Software

Ver mais: r-rx, p. n. g. engineering, defining you, circle graphics, 3 point circle formula, 3 point circle equation, p 3d, image of a circle, x-plane, wx, uz, rz, RX, mathematical m, mathematical equation, face r, dx, projection projection, php image orientation, need formula, arbitrary, presentation engineering, plot php, curve project, camera engineering project

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( 7 comentários ) Barden Ridge, Australia

ID do Projeto: #3052830

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DonCastelano

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