Stereographic Definition and 27 Threads

Stereoscopy (also called stereoscopics, or stereo imaging) is a technique for creating or enhancing the illusion of depth in an image by means of stereopsis for binocular vision. The word stereoscopy derives from Greek στερεός (stereos) 'firm, solid', and σκοπέω (skopeō) 'to look, to see'. Any stereoscopic image is called a stereogram. Originally, stereogram referred to a pair of stereo images which could be viewed using a stereoscope.
Most stereoscopic methods present two offset images separately to the left and right eye of the viewer. These two-dimensional images are then combined in the brain to give the perception of 3D depth. This technique is distinguished from 3D displays that display an image in three full dimensions, allowing the observer to increase information about the 3-dimensional objects being displayed by head and eye movements.

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  1. R

    Vector Field associated with Stereographic Projection

    I identified $$(\Phi_{SN})_{*})$$ as $$J_{(\Phi_{SN})}$$ where J is the Jacobian matrix in order to $$(\Phi_{SN})$$, also noticing that $$\frac{\partial}{\partial u} = \frac{\partial s}{\partial u}\frac{\partial}{\partial s} + \frac{\partial t}{\partial u} \frac{\partial}{\partial t} $$, I wrote...
  2. sbmarantz

    Plot a stereographic hypercube in a Mac's Grapher.app?

    Hello everyone, first post here. I don't need to do this in Grapher.app (the default graphing calculator on every Mac), but it is an elegant humble little app, and I have seen the hypercube projected using it here. I really would love to get the equations and expressions in my own file on my...
  3. FallenApple

    I Pole in Stereographic Projection

    So the circle minus the pole is homeomorphic to the number line. Does that mean that the pole itself represents a number that doesn't exist on the real line? After all, the pole certainly exists and yet is the only point that isn't mapped.
  4. T

    B Stereographic projection and uneven scaling

    Lets assume we are mapping one face of earth. we place a plane touching the Earth at 0 lattitude and 0 longitude. Now we take the plane of projection. suppose that we expand the projection unevenly. The small projectional area of a certain lattitude and longitude is expanded by a factor which is...
  5. S

    A Stereoscopic Images and Distance Between Objects

    Hello Experts, I leaned that using a sterescopic cameras (generates 2 photos) one can measure the distance to any object in the image produced by the camera. For example, if I take a picture of a lamp post using a stereoscopic method, I can determine the Distance from the camera to the lamp...
  6. I

    Rotations around the x and y axes of stereographic sphere

    Homework Statement Show that the equations $$ \delta \phi = \cot \theta \cot \phi \delta \theta, \quad \delta \phi =- \cot \theta \tan \phi \delta \theta$$ represent rotations around the x and y axes respectively of a stereographic sphere. Both these two rotations map the sphere on itself and...
  7. A

    A Project img on X-Y surface to a cylinder placed in center....

    Hi , I came across a problem ,I've search a lot but couldn't exactly find the solution. here is my problem: suppose there is an image ( I call it IMG_A),place IMG_A in the X-Y plane , put a mirror cylinder at the center of IMG_A. what we see in the cylinder mirror is a deform image (I call it...
  8. S

    Projection stereographic and second fundamental form

    Let r:R2 →R3 be given by the formula Compute the second fundamental form with respect to this basis (Hint: There’s a shortcut to computing the unit normal n). I can't find thi shortcut, does anyone help me? I'm solving it with normal vector and first and second derivate, but I obtained...
  9. M

    Higer dims: Electromagnetic field lines and stereographic projection

    I've noticed that electromagnetic field lines are very similar to stereographic projection of 3D sphere on 2D surface. Pictures below. In such comparison, electric field represents longitude and magnetic field represents latitude. For more visualization see...
  10. M

    Earth stereographic projection line intersection

    Hi, Consider you are standing upright and pointing your finger at the ground. Where does the vector coming off the tip of your finger arrive when it hits ground level on the other side of the Earth? ..Think as if you were going to imperviously dig a hole through the Earth and could travel...
  11. A

    Stereographic projection in de Sitter cosmological model

    We know stereographic projection is conformal but it isn't isometic and in general relativity it can not be used because in this theory general transformations must be isometric. But de sitter in his model (1917) used it (stereographic projection) to obtain metric in static coordinates. How...
  12. M

    Stereographic Projection of Circular Hodographs in Momentum 4-Space

    Dear all, I want to prove that a circular hodograph (planetary orbit in momentum 3-space) stereographically projects onto a great circle of a 3-sphere in momentum 4-space. The equation for the hodograph is given by: \begin{equation} \left( \frac{mk}{L} \right)^2 = p_1'^2 + \left( p_2' -...
  13. N

    How are Stereographic Projections Derived in Differential Geometry?

    In cartesian coordinates (x.y,z) on the and (X,Y) on the plane, the projection and its inverse are given by the following formulae: (X,Y)=(x/1-z,y/1-z) (x,y,z)=(2X/1+X^2+Y^2, 2Y/1+X^2+Y^2, -1+X^2+Y^2/1+X^2 +Y^2) This relates to the field of differntial geo.Anybody have a proof to where thes...
  14. W

    How to Compute r in Stereographic Projection from R^4 to R^3?

    I am computing a stereographic projection in R^4 and i think i am correct in setting x=rcos(x)sin(y) y=rsin(x)sin(y) z=rcos(y) but can't see how to compute r as I do not know to visualise it graphically as was possible in R^3, any help would be greatly appreciated
  15. mnb96

    Finding the Metric in Stereographic Projection

    Hello, if we consider the stereographic projection \mathcal{S}^2\rightarrow \mathbb{R}^2 given in the form: (X,Y) = \left( \frac{x}{1-z} , \frac{y}{1-z} \right) how can I find the metric in X,Y coordinates? -- Should I first express the projection in spherical coordinates, then find...
  16. G

    Proving Homeomorphism for Stereographic Projection onto S1-{(1, 0)}

    Homework Statement Show that the map f : R--> S1 given by f(t) =[(t^2-1)/(t^2+1), 2t/(t^2+1)] is a homeomorphism onto S1-{(1, 0)}, where S1 is the unit circle in the plane. I know this is a stereographic projection, but I do not know how to show that it has a continuous inverse. I am...
  17. M

    Mobius Transformations and Stereographic Projections

    Homework Statement Hi all - I've been battering away at this for an hour or so, and was hoping someone else could lend a hand! Q: Show that any Mobius transformation T not equal to 1 on \mathbb{C}_{\infinity} has 1 or 2 fixed points. (Done) Show that the Mobius transformation corresponding...
  18. D

    Stereographic Projection for general surfaces

    Stereographic Projection for "general" surfaces First off, sorry if this is in the wrong forum. I came across this while studying computer vision, but it's of a somewhat mathematical nature. Please move it if it's in the wrong place. In the book I'm reading*, stereographic projection is used...
  19. D

    Why does stereographic projection preserve angles but not area?

    Why stereographic projection preserves angles between curves but does not preserve area?
  20. E

    Inverting parabolic and stereographic coordinates

    Homework Statement Given the parabolic co-ordinate system defined, given Cartesian coordinates x and y, as $\mu=2xy$ $\lambda = x^2-y^2,$ find the inverse transformation x(\mu, \lambda) and y(\mu,\lambda). Homework Equations None The Attempt at a Solution We compute...
  21. S

    What Do Colors and Shapes Represent in Stereographic Projections?

    Hello, Can anyone tell me what the triangles, squares, and ovals mean in the projection on page 19? Does this have something to do with the directions for the third axis? On the next page several of the symbols are black. What significance does this have, also? Thanks -scott "[PLAIN...
  22. M

    How Do You Solve a Stereographic Projection Problem in Mathematics?

    Urgent Stereographic projection question... Homework Statement Given the unit sphere S^2= \{x^2 + y^2 + (z-1)^2 = 1\} Where N is the Northpole = (0.0.2) the stereographic projection \pi: S^2 \sim \{N\} \rightarrow \mathbb{R}^2 carries a point p of the sphere minus the north pole N onto the...
  23. M

    How Does Stereographic Projection Map Spheres to the Complex Plane?

    Hi there, Look at the topic from my textbook "Stereographic Projection". Please inform me if I have understood it correctly :) Lets take specific example from my textbook S' = \{(x,y,z)|x^2 + y^2 + (z-1)^2 = 1\} is a sphere where N = (0,0,2) and P = (x,y,z) can be viewed as steographic...
  24. C

    Inverse of the Stereographic Projection

    In any book on differentiable manifolds, the stereographic projection map P from the n-Sphere to the (n-1)-plane is discussed as part of an example of how one might cover a sphere with an atlas. This is usually followed by a comment such as "it is obvious" or "it can be shown" that the inverse...
  25. P

    Geometry - Stereographic projection.

    I know if a cirlce (on S^2) does not contain N (0,0,1) then it is mapped onto the plane H as a circle. Now say the circles on S^2 are lines of latitude. When mapped by the stereographic projection they are cirlces in R^3 on the plane H. Now the only thing I am not sure on is, my claim: When...
  26. P

    Geometry - Stereographic projection

    I know if a cirlce (on S^2) does not contain N (0,0,1) then it is mapped onto the plane H as a circle. Now say the circles on S^2 are lines of latitude. When mapped by the stereographic projection they are cirlces in R^3 on the plane H. Now the only thing I am not sure on is, my claim: When...
  27. T

    Can Stereographic Projection from Unit Sphere to Plane be Proven as Injective?

    So I'm trying to prove that the map f(x,y,z) = \frac{(x,y)}{1-z} from the unit sphere S^2 to R^2 is injective by the usual means: f(x_1,y_1,z_1)=f(x_2,y_2,z_2) \Rightarrow (x_1,y_1,z_1)=(x_2,y_2,z_2) But i can't seem to show it... :frown: I end up with the result that...
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