Mapping Definition and 404 Threads

Texture mapping is a method for defining high frequency detail, surface texture, or color information on a computer-generated graphic or 3D model. The original technique was pioneered by Edwin Catmull in 1974.Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene.

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  1. C

    Mapping Coordinate Systems Using Quaternions

    During the course of working with inertial measurement units (IMU) I have run into a problem. The issue is that an IMU reports accelerations relative to the IMU's orientation rather than it's initial orientation. The IMU's initial orientation is the identity quaternion (1,0,0,0). All changes...
  2. J

    Cyclic Group - Isomorphism of Non Identity Mapping

    Homework Statement Prove that if G is a cyclic group with more than two elements, then there always exists an isomorphism: ψ: G--> G that is not the identity mapping. Homework Equations The Attempt at a Solution So if G is a cyclic group of prime order with n>2, then by Euler's...
  3. W

    Mapping Class Group of Contractible Spaces

    Hi all, Isn't the mapping class group of a contractible space trivial (or, if we consider isotopy, {+/-Id})? Since every map from a contractible space is (homotopically)trivial.
  4. S

    Why Does Complex Mapping T(z) = Az + B Fail Linearity?

    Hello, Given the complex linear mapping: T(z) = Az + B where A is real and B is complex. However trying to show that T(a * z1 + z2) = a * T(z1) + T(z2) does not work which implies the mapping is not linear? Why does not this rule apply here? Thanks.
  5. I

    Counting the distinct values of a modular mapping

    Hello, first of all, sorry if my question is either trivial or imprecise, I'm from the engineering domain :) I need to know how many different values the following pair can take: \left(a\cdot i + b\cdot j\right) \bmod n_1 \left(c\cdot i + d\cdot j\right) \bmod n_2 as (i,j) spans \mathbb{Z}^2...
  6. Math Amateur

    Demonstrating that a mapping is injective

    I am reading Dummit and Foote, Section 10.5 : Exact Sequences - Projective, Injective and Flat Modules. I am studying Proposition 28 (D&F pages 387 - 388) In the latter stages of the proof of Proposition 28 we find the following statement (top of page 388): "In general, Hom_R (R, X) \cong X...
  7. Math Amateur

    MHB Demonstrating that a mapping is injective

    I am reading Dummit and Foote, Section 10.5 : Exact Sequences - Projective, Injective and Flat Modules. I am studying Proposition 28 (D&F pages 387 - 388) In the latter stages of the proof of Proposition 28 we find the following statement (top of page 388): "In general, Hom_R (R, X) \cong X...
  8. Rahulr2k

    Difference between direct mapping and set associated mapping

    What is set associated mapping and What are the difference between direct and set associated mapping
  9. F

    Can This Plasmid Map Be Created with Given Restriction Enzyme Data?

    Homework Statement Use the following data to create a plasmid map. Number of base pairs for each restriction enzyme A: 20 B : 11 6 3 A & B: 7 6...
  10. S

    Conformal Mapping: Find Function to Map Between Two Parallel Lines

    Homework Statement Find function that maps area between ##|z|=2## and ##|z+1|=1## on area between two parallel lines. Homework Equations The Attempt at a Solution I don't know how to check if my solution works for this problem? I used Möbious transformation...
  11. D

    Conformal mapping of an infinite strip onto itself

    Homework Statement Find a conformal mapping of the strip ##D=\{z:|\Re(z)|<\frac{\pi}{2}\}## onto itself that transforms the real interval ##(-\frac{\pi}{2},\frac{\pi}{2})## to the full imaginary axis.The Attempt at a Solution I tried to map the strip to a unit circle and then map it back to the...
  12. A

    MHB Map of Area Bounded by y=5x & y=-3x in Upper Plane

    what is the map of the area bound by y=5x and y=-3x in the upper half plane, under w=1/z we have the lines : $ z(t) = t + 5t i $ , and the line $z(t) = t - 3ti $ Fist line $\displaystyle w_1 = \dfrac{1}{t+5ti} = \dfrac{1}{26t} - \dfrac{5i}{26t} $ Second $\displaystyle w_2 = \dfrac{1}{t -...
  13. B

    Solving the Set Mapping Problem: How Many Is Enough?

    Let say i have two sets of numbers A and B. and I want to assigne to each number from A two slosest numbers from B. What i would do is to pick an elements from A and then go through the entire B set and find two closest. now if i go the other way arround in orderd to achieve the same result i...
  14. I

    Mapping Gases Over a City: Theoretical Experiment

    I am looking for a way to map gases over a city, what are some ways I could do that? This is a theoretical experiment so cost is not an issue. Thanks in advance
  15. M

    MHB Collaborative Mind Mapping for Abstract Algebra: Building a Visual Blueprint

    Hello I've been doing a mind map of Abstract Algebra. A mind map is a visual representation of a subject, like algebra, organic chemistry, etc. , in a way that makes the subject structured in a more intuitive way, without losing the logical component. It's a map of the subject that make the...
  16. A

    Prove the Contraction Mapping Theorem.

    Prove the Contraction Mapping Theorem. Let ##(X,d)## be a complete metric space and ##g : X \rightarrow X## be a map such that ##\forall x,y \in X, d(g(x), g(y)) \le \lambda d(x,y)## for some ##0<\lambda < 1##.Then ##g## has a unique fixed point ##x^* \in X ##, and it attracts everything, i.e...
  17. J

    Electric Field Mapping Lab. Qualitative questions.

    For an upcoming lab I will be mapping out the equipotential lines in an electric field with an isolated conductor in it. The conductor is a hollow cylinder. I have attached a crude paint drawing of the apparatus. The lab asks some qualitative questions that I would like to knock out before hand...
  18. G

    Mapping question I don't understand

    Hi I uploaded the question and its answer first of all I am not good at all in mapping I don't understand it that much like here we want the output of the function under that specific domain that's what we want to see. I understand until PI < alpha < 5/2 * PI but I don't understand how did he...
  19. P

    Conformal mapping w=1/z - question.

    Hi, Homework Statement I'd like to show that the mapping w=u+iv=1/z tranforms the line x=b in the z plane into a circle with radius 1/2b and center at u=1/2bHomework Equations The Attempt at a Solution z*w=1=(b+iy)(u+iv) → 1=|(bu-yv)+i(bv+yu)| → u2+v2=1/(b2+y2) Now, a circle with radius 1/2b...
  20. S

    For a linear mapping F, how do I define F^2?

    Hi. This is a homework question, so I can't ask or give out too much info. SO, there is a linear mapping F, and it is given that F=F^2. Can I assume that everything about F, i.e. dimension, kernel, image, etc, is exactly the same for F^2? Or does it just mean that given a vector v, F(v) =...
  21. alyafey22

    MHB Mapping and inverse mapping of open sets and their complements

    Assume that f: E \to Y \,\,\, , E \subset X then can we say that f(E^c)=f(E)^c what about the inverse mapping f^{-1}: V \to X \,\,\, , V\subset Y do we have to have some restrictions on f and its inverse ? My immediate answer is that we have to have a bijection in order to conclude that but I...
  22. A

    Phonon Interactions & Brillioun Zone Mapping

    This occur when two phonons interact and the sum of their momenta add to a new wavevector outside the new Brillioun zone. The resulting wavevector is then mapped back into the Brillioun zone by subtraction of a suitable reciprocal lattice vector. I don't think I understand the physics in all of...
  23. N

    MHB Understanding Mapping: Domain, Range & W Subset of C

    Hi, This is a little different from most questions in that it's not something I want to solve, but rather hoping I could get a little clearer explanation on what mapping is and why/when we use it? I'm soon to go over conformal maps, but I don't think i understand anything to do with mapping as...
  24. lpetrich

    Eukaryote high-level evolution - have we succeeded in mapping it?

    The overall phylogeny of eukaryotes has long been a difficult and contentious subject, almost as bad as the phylogeny of prokaryotes. One could recognize some well-defined groups, but that was about it. But as biologists learned out to sequence proteins, and then nucleic acids, they got a...
  25. I

    Question about isomorphic mapping on direct sums?

    The identity map on the direct sum of V1 and V2 would be i1 composed with p1 + i2 composed with p2. Would such an identity map exist for an infinite direct sum? And an analogous mapping for a direct product?
  26. B

    Struggling to understand vecot coordinate mapping.

    I am somewhat puzzled after reading that polynomials can be vectors, this concept confuses me. For instance, they can say that a basis for polynomials P_2 can be. B=\{1+t^{2},t+t^{2},1+2t+t^{2}\} In this case will the mapping [1+t^{2}]_{B} be [1,0,0] or [1,0,1]?
  27. alyafey22

    MHB Continuous mapping of compact metric spaces

    Let $f$ be a continuous mapping of a compact metric space $X$ into a metric space $Y$ then $f$ is uniformly continuous on $X$. I have seen a proof in the Rudin's book but I don't quite get it , can anybody establish another proof but with more details ?
  28. M

    Linear algebra.Kernel of a linear mapping

    Let ##L## be a linear operator ::##L(A)= Tr(A)## where ##Tr(A)## is the trace of a square matrix Find a basis of the kernel of L. Any help would be really appreciated . thanks in advance
  29. M

    Linear algebra- Inverse of a linear mapping

    Homework Statement Let L: V →V be a linear mapping such that L^2+2L+I=0, show that L is invertible (I is the identity mapping) I have no idea how to solve this problem or how to start,I mean this problem is different from the ones I solved before, the answer is "The inverse of L is -L-2 "...
  30. D

    Mapping Rotations of Relative Axes to Fixed Axes

    So I have been trying to figure out some orientation data that I gather from a triaxial gyroscope, and figure out my orientation using only initial conditions and angular velocity from the gyroscope's current axes. The data is all relative to the current orientation, so if I rotate the device...
  31. J

    Mapping of algebraic function to Riemann surface?

    When we map the algebraic function, w(z), to a Riemann surface we essentially create a new "Riemann" coordinate system over a surface that is called the "algebraic function's Riemann surface". This mapping allows one to create single-valued functions, f(z,w), of the coordinate points over...
  32. R

    Mapping Euler spiral (clothoid) parameters

    Hi... first post here! Sorry if not in the right place. I am trying to decode the parameters for an xml file format and I would appreciate help in interpreting some parameters. I know the thing specified is a "transition curve" or clothoid curve, as the transition between a straight path and...
  33. O

    Is f(x) a Contraction Mapping?

    Hello All: I am working on a function given as f(x) = 10/x + (1/20)x^2 for x such that 0≤x≤10. What can be said about the contraction mapping property of f(x)=x? If it is not a contraction map, is there any way to make modifications on the function or the interval and prove a contraction mapping...
  34. STEMucator

    Mapping Problems to Prove TSP Solves HCP

    Homework Statement I wasn't sure where to post this in particular, so I apologize if this is in the wrong section. I've been getting interested in the topic of problem mapping lately. I came across this problem while reading and I'm not quite sure if I have the right idea or not. The...
  35. Fernando Revilla

    MHB Contraction mapping (Maryam Ishfaq's question at Yahoo Answers)

    Here is a link to the question: Prove that a contraction T on a metric space is a continuous mapping? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  36. N

    Mapping 4D torus onto 4-sphere non-trivially

    Hello, I'm trying to construct an explicit map that takes the 4D torus to the 4-sphere such that the wrapping is non-trivial (i.e. homotopically, i.e. you can't shrink it continuously to zero). More concretely, I'm looking for \phi: T^4 \to S^4: (\alpha,\beta,\gamma,\delta) \mapsto (...
  37. S

    Kernel and Range of a Linear Mapping

    Homework Statement Find the kernel and range of the following linear mapping. b) The mapping T from P^{R} to P^{R}_{2} defined by T(p(x)) = p(2) + p(1)x + p(0)x^{2} The Attempt at a Solution I'm not sure how to go about this one. Normally I would use the formula T(x) = A * v...
  38. N

    Is that mapping the homomorphism?

    Homework Statement Let G be a group and let Aut(G) be the group of automorphisms of G. (a) For any g \in G, define \phi_{g}(x) = g^{-1}xg. Check that \phi_{g}(x) is an automorphism. (b) Consider the map: \Phi:G \rightarrow Aut(G) g \mapsto \phi_{g} Check that \Phi is a...
  39. U

    Show that the linear transformation matrix is a contraction mapping

    Homework Statement Show that the following linear transformation matrix is a contraction mapping. \begin{bmatrix} 0.5 & 0 & -1 \\ 0 & 0.5 & 1 \\ 0 & 0 & 1 \end{bmatrix} I don't know how to make that into a matrix, but it is a 3x3 matrix. The first row is [.5 0 -1] the second row is [0...
  40. diegzumillo

    Electrostatics - method of conformal mapping (from Landau)

    I'm studying Landau's Electordynamics of continuous media and, although I like how succinct it is, sometimes it is too succinct! I'm having trouble with a particular passage, so I'll just try to summarize the section up until the part I don't understand. The topic at hand is electrostatic field...
  41. O

    MHB Fixed point for a complex mapping.

    W= z+2 /z-2 drawing mapping find image in w plane line Re(z)constant and im(z)=constant find fixed point from mapping In my textbook have just W = z-1 / z+1 . Thank a lot for your help.
  42. P

    Implicit Mapping Theorem for a Surface

    The question, from Edward's Advanced Calculus (which is becoming a rather frustrating book), asks if the following surface can be represented as a function of ##z(x,y)## near the point ##(0,2,1)##: xy - ylog(z) + sin(xz) = 0 Naturally, this should invite me to use the Implicit Mapping...
  43. R

    How to show that a locally diffeomorphic mapping from R to R is open?

    Let f: R -> R be a local diffeomorphism (diffeomrophism in a neighborhood of each point). Show that the image of R under f is an open interval. Furthermore show that f is a diffeomorphism of R on to f(R). Ok, here is what I am thinking.. that since we are dealing with a "diffeomorphism" we...
  44. M

    Mapping Changes in Current to Voltages

    What's the trick to convert changes in current to some voltage equivalent? 50% increase in current --> 50% increase in voltage Can it be done? What I'm doing is trying to take a photoresistor and have it act as an analog input on a ADC however the ADC is voltage based. :-\
  45. G

    Analytic mapping from disk to disk must be rational

    Let f(x) be a function which is defined in the open unit disk (|z| < 1) and is analytic there. f(z) maps the unit disk onto itself k times, meaning |f(z)| < 1 for all |z| < 1 and every point in the unit disk has k preimages under f(z). Prove that f(z) must be a rational function. Furthermore...
  46. G

    Proving mapping must be a rational function (complex analysis)

    Homework Statement Let f(x) be a function which is defined in the open unit disk (|z| < 1) and is analytic there. f(z) maps the unit disk onto itself k times, meaning |f(z)| < 1 for all |z| < 1 and every point in the unit disk has k preimages under f(z). Prove that f(z) must be a rational...
  47. N

    Conformal Mapping and flow normal to ellipse

    Hi, Given that the flow normal to a thin disk or radius r is given by \phi = -\frac{2rU}{\pi}\sqrt{1-\frac{x^2+y^2}{r^2}} where U is the speed of the flow normal to the disk, find the flow normal to an ellipse of major axis a and minor axis b. I can only find the answer in the...
  48. B

    Mapping an isomorphism b/w 2 grps

    I googled this but couldn't find a clear answer. Is every invertible mapping an isomorphism b/w 2 grps or does it have to be linear?
  49. D

    Vim Mapping Umlaute: Tips & Fixes

    When I am editing German Latex files in vim using a us keyboard, I would like to map "a to a-umlaut etc. I added corresponding imap commands in my vimrc and they work in principle. However I have to type "a" after """ at a certain speed, if not, the cursor jumps from before """ to after it...
  50. M

    MATLAB How Do You Plot High Resolution Earthquake Maps in Matlab?

    I'm trying to plot positions of earthquakes on a map. The primary goal is to make Matlab plot a map so I can put the positions of earthquakes on it. I've read through the help section for Matlab's Toolbox but to be honest I'm still confused about it. Has anyone used Mapping Toolbox to know...
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