What is Mapping: Definition and 404 Discussions

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. J

    Mapping a building for use in game (RADAR?)

    Hi guys I hope I'm in the right subforum. I was thinking of a way to map a house or outside area with radar or some other method, and then using that info to create a map for a game. So my question is, what are the different methods available for sensing the surrounding area and creating a...
  2. K

    Are f and g Injective and Surjective if g\circf is Injective or Surjective?

    Could anybody help me check whether my judgements ture or false? (MJ = My Judgement) Suppose f maps A into B, and g maps B into C 1. If f and g are injective, then g\circf is injective; (MJ)but that when g\circ f is injective, the injectivity of f and g are unsure. 2. If f and g are...
  3. S

    Conformal Mapping (unit circle => ellipse)

    I'd like to map the open unit circle to the open ellipse x/A^2 + y/B^2 = 1. How would I go about doing this? I really have no idea how to go about doing these mappings. I'm working with the text Complex Var. and Applications by Ward and Churchill which has a table of mappings in the back...
  4. F

    Showing a mapping is onto and/or one to one

    Hello, I have a general question about isomorphisms of vector spaces. I understand the concepts of mappings being one to one, and onto, but how do I go about SHOWING that a mapping is either one to one, onto, one or the other or both? For example, the mapping R^2-->R^2 defined by f(x,y) =...
  5. C

    Understanding the Nonlinear Mapping of Analytic Functions

    Homework Statement This is an example in Advanced Engineering Mathematics by Erwin Kreyszig p.675 which I don't understand. If you map w=z^2 using Cartesian Co-ordinates, w is defined as w=u(x,y)+iv(x,y), therefore, u=Re(z^2)=x^2-y^2 and v=Im(z^2)=2xy. The function is graphed using u and v...
  6. G

    Solving electrostatic, rotationally symmetric 3D problem with conformal mapping?

    I heard that one can solve 2D problem with conformal mapping of complex numbers. Is it possible to use this method for 3D axial-rotationally symmetric problems (which are effectively 2D with a new term in the differential equation)?
  7. O

    Mapping Mathematical Subjects: Prerequisites & Dependencies

    I'm trying to map out how certain mathematical subjects depend on each other, i.e. which subjects could be described as prerequesites for which other subjects, in the sense that the former define needed or helpful concepts for the latter. In a crude ascii diagram, which might look messed up...
  8. K

    Inverse mapping theorem , Transformations

    A quick question this time... Example: Let (u,v)=f(x,y)=(x-2y, 2x-y). Find the region in the xy-plane that is mapped to the triangle with vertices (0,0),(-1,2),(2,1) in the uv-plane. Solution: (0,0)=f(0,0), (-1,2) = f(5/3,4/3), and (2,1)=f(0,-1), the region is the triangle with...
  9. K

    Inverse mapping theorem & local inverses

    [Related concepts: Inverse mapping theorem, transformations and coordinate systems] 1) For each of the following transformations (u,v) = f(x,y), (i) compute det Df, (ii) find formulas for the local inverses of f when they exist. a) u=x^2, v=y/x b) u=(e^x) cos y, v=(e^x) sin y I got...
  10. D

    Conformal Mapping Homework: f(z) = 1/(z-1), c=i

    Homework Statement "Study the infinitesimal behavior of f at the point c. (In other words, use the conformal mapping theorem to describe what is happening to the tangent vector of a smooth curve passing through c.)" f(z) = 1/(z-1), c=i Homework Equations |f'(c)| and arg f'(c)...
  11. N

    Mapping torus is an (m+1)-manifold

    Homework Statement Let X be an m-manifold. Let M(f) be the space obtained from X\times [0,1] by gluing the ends together using (x,0)\sim (f(x),1). Show that if M is an m-manifold then M(f) is an (m+1)-manifold. The Attempt at a Solution Since X has an atlas \{ (U_\alpha,\varphi_\alpha) \}...
  12. T

    How Do You Calculate Recombination Frequency and Map Distance in Genetics?

    I would appreciate help with this problem, if at all possible! Homework Statement Snapdragons, homozygous for the recessive allele ls of the leaf form gene, have serrated leaves, the normal allele l+ is dominant and responsible for a smooth leaf phenotype. Individuals homozygous for the...
  13. J

    How can I create a conformal mapping between a square and triangle?

    When trying to solve one problem (my own, not an exercise), I encountered the need for a conformal mapping between a square [0,1]^2 and a triangle (0,0)-(1,1)-(2,0), so that the side (0,0)-(0,1) of the square gets mapped into a point (0,0), and the three other sides become the sides of the...
  14. F

    Flow Mapping Theorem and Obstacles

    Hi All I have one final question that's related to flow problems with obstacles. Any help would be greatly appreciated as I am finding fluid flows extremely difficult. "Examinations are formidable even to the best prepared, for the greatest fool may ask more than the wisest man...
  15. L

    Function Mapping to Open Intervals

    Hello, I'm working on some questions and I need some further explanation; First I must Consider the open interval (0,1), and let S be the set of point in the open unit square; that's is, S={(x,y):0<x,y<1}. Question (a) says Find a 1-1 function that maps (0,1) into, but not necessarily onto, S...
  16. U

    Function vs mapping vs transformation

    During learning linear algebra, I have met at least three items (kind of action in my own word): function, mapping and transformation. What are the relation and difference among them? e.g. Given y=f(x), we can say f map x to y, f transform x to y and the function of x is y. In saying the...
  17. S

    Need help with my course on memory mapping and stuff

    I have got a begginner's course in computer organisation this semester. The course consists of the basic stuff like types of memories and memory hierarchy with the detailed description of each etc etc. Now, what i really don't get is memmory mapping and how exactly data is read and written on...
  18. B

    Free 3-D EM Software for Modeling Transformers and Mapping Poynting Vectors

    Does anybody know of free 3-D EM software so that I can model a transformer? In particular, I'm interested in mapping Poynting vectors. Thanks.
  19. S

    Medical Mapping Intention with Reflex Supression

    When you reach out to grab something that is hot, or you receive an unexpected electrical shock, the normal human reaction to withdrawal the limb is reflexive, or so I understand. As such, no signal reaches the brain before the reflex begins - if this is incorrect, let me know. However, given...
  20. P

    Understanding Mappings between Quotient Rings

    Homework Statement If I was to map elements in R/A to R/B via the function p. So p:R/A -> R/B Can I assume there are no elements in R/B before the mapping? Or is it more there are elements in R/B already before the mapping. However during the mapping, I highlight each element in R/B...
  21. P

    Exploring Mapping Conditions: Can Elements be Left Unmapped?

    Homework Statement Can there be a mapping that may not map any elements from one domain to another? The reason is that the mapping has a condition. For example, it will only map elements if the one in the domain are related in some way to the element they are mapped to (i.e congruence via a...
  22. P

    How do you define a mapping f:K->N

    Homework Statement How do you define a mapping f:K->N with K={0} N is the integers. that maps the element 0 to every single single element in N? ie. 0->-n, ... , -2, -1, 0, 1, 2, ... , nIs that even possible? The mapping Z->Z by multiplying each element in Z by 0 is a legitamate mapping...
  23. mattmns

    Can Nearby Contractions Imply Nearby Fixed Points?

    Here is the question from our book: ------- Let (X,d) be a complete metric space, and let f:X\to X and g:X\to X be two strict contractions on X with contraction coefficients c and c' respectively. From the Contraction Mapping Theorem we know that f has some fixed point x_0, and g has some fixed...
  24. PhysicsIsFun

    Conformal Mapping of Aerofoil at incidence

    Does anyone know what the conformal mapping of an aerofoil at incidence is? Does it use the Joukowski transformation? Or something else.. Thanks
  25. D

    Equipotential Lines and field mapping

    Equipotential Lines! I recently did a lab in class that dealt with electric field mapping (very similar to http://physics.nku.edu/GeneralLab/211%20Elect%20Pot.%20&%20Field%20Map.html) and i have to write a lab report now.. I don't understand why the equipotential lines are always perpendicular...
  26. R

    Draw Lattice Diagram for K: Solving Algebra I Mapping Homework

    Homework Statement K = {x C S7 | 2x=2, {1,4}x={1,4}, {1,5,7}x={1,5,7}}. Draw Lattice Diagram for K.2. The attempt at a solution I've looked at this for about 30 minutes and came to the conclusion that there are 140 unique solutions to this mapping, and I know for a fact that the professor...
  27. U

    Mapping an Equal Potential Field

    Homework Statement For this lab, we have one wire hooked up to the positive terminal of a battery pack and another hooked up to the negative terminal. Each of those is attached to a weight and placed in salt water. Another wire is hooked up to a voltmeter which is then attached to the...
  28. N

    Mapping Complex Dimensions to 3D Surface Visualization

    I am trying to do a computer visualization of a surface in complex dimensions 2. I choose simple quintic equation: z^5_1 + z^5_2 = 1 I also implemented algorithm for producing plots of 3D surfaces that are defined with algebraic equations. It is called Marching Cubes and it simply checks how...
  29. E

    Complex Mapping - Express x & y in terms of u & v

    w = 1/(z+2j): w = u + jv, z = x+jy Its not hard to express this in terms of z... z = 1/w - 2j But how can i go about expressing x and y and terms of u and v Substitution of those above terms gets you x + jy = 1/(u + jv) - 2j I am not clear on the next steps Any help is much...
  30. P

    LINEAR ALGEBRA: Linear Mapping

    I have the linear mapping Pw(x). How can I prove that: ||P_w(x)||^2 = \Sigma (<x, x_i>)^2 Where the sum is from i = 1 to k x is any vector which is an element of R^n I have tried expanding ||P_w(x)||^2 but it doesn't seem to give me the right side of the equation. Is there any other...
  31. mattmns

    Exploring Infinity in Computer Mapping: A Problem

    This issue of infinity (undefined?) keeps coming up in the following problems. For example, the following question: Computer the image of the sector 0 \leq r \leq 1, 0 \leq \theta \leq \pi, under the map ln(z). ------------- So I first graphed this thing in the x,y (z-plane) and obviously...
  32. M

    Prove Mapping from Set to Itself: 1-1 & Not onto iff Onto & Not 1-1

    Prove that there is a mapping from a set to itself that is one-to one but not onto iff there is a mapping from the set to itself that is onto but not one-to -one. Since this is a 'iff' proof, so I must prove the statementlike two 'if' statements. Let g:S ---> S. Assume that g is 1-1...
  33. S

    Mapping of Functions from S to T: n<=m

    There are 2 parts to this question: How many functions are there from a set S with n elements to a set T with m elements? Assume n<=m, how many one-to-one functions are there from S to T? I am pretty sure that the answer to the first part is mn. So if there are 3 elements in the first...
  34. T

    Conformal mapping. From an ellipse to a rectangle

    Is it possible to transform an ellipse x^2/a^2 + y^2/b^2 = 1 ("a" minor or major semiaxis) Into a rectangle? If so, how can I do it? I am not very familiar so please explain all the details. I know the transformation from a circle to an airfoil, but not this one.
  35. S

    What are the applications of the Riemann Mapping Theorem?

    so i know what it is (i think lol) ... but what are its applications?
  36. C

    Rank condition in the Implicit Mapping Theorm

    Hi there. I've recently come across the Implicit Mapping Theorm in my studies and noticed that there is a condition that the rank of the image must be the maximum possible. I'm not directly seeing why this condition is needed, so I was wondering if anyone could provide me with an example of why...
  37. T

    Gene mapping - what of combinatorics?

    Hey, so in 2003, it was announced that the human genome was more or less mapped. The difference between individual humans is about 0.2 percent of the 3 000 000 000 genes we have. So somehow, this percentage should account for all of the human variations that aren't dependent on environment...
  38. T

    Understanding Electric Field Mapping for Oppositely Charged Point Charges

    If two oppositely charged point charges are separated, with a fairly large circular (spherical) conductor between them, then the equipotential surfaces will kind of wrap around the contour of the conductor, correct? And the electric field would look like it does for a normal dipole, with the...
  39. Loren Booda

    Phase space: a one-to-one mapping with all quantum dynamics?

    Does the history of wave packets translate exactly onto infinite phase space, or is phase space incompletely (or redundantly) covered by quantum mechanics?
  40. C

    Mapping Notation Mapping Rule: Understanding Inversion & Shifts

    Mapping Rule Say I have the function y = 2 \sin 3(x - 20) and the corresponding mapping notation (x, y) \rightarrow (\frac{1}{3}x + 20, 2y) (which I assume is correct.) How come I take the inverse of the amplitude (2) and horizontal "compression" (3), and how come a negative phase shift moves...
  41. B

    DOFs in coordinate mapping if metrics specified?

    I am trying to determine a mapping between two coordinate systems, given only the metric tensor written for each system. How much freedom do I have available in specifying the mapping once the metrics have been given? I know that the transformation equations of the metric tensor components...
  42. C

    Solving Conformal Mapping Flow Problem

    Hi everyone, Let me set the scene. I'm writing a program to model the flow of an ideal fluid around various singularities using the complex potential and then using conformal transformations to map boundaries into new shapes. It's very nearly done but one of the transformations (what appears...
  43. V

    High Rez EMF Mapping: Seeking Advice

    Greetings, This was posted in the Classic Physics section, reposted here in Quantum section in case someone here may have some experience in EMF mapping. I am currently working on an interesting experiment on crystalized metal and I need to find a way to get a detailed map of an...
  44. V

    High rez electromagnetic field mapping

    Greetings, I am currently working on an interesting experiment on crystalized metal and I need to find a way to get a detailed map of an electromagnetic field when current is induced into a metal sample. I found the basic 2D approach of using conductivity paper and Ag ink to be useless as it...
  45. H

    Mapping a generic quadrilateral onto a rectangle (in 2 dimensions)

    Problem: I have a computer image of a grid "square" from an aviation chart. The "square" is actually approximately rectangular, but the left and right sides aren't quite parallel and the top and bottom sides are parallel but very slightly curved. I will assume/pretend that the top and...
  46. R

    Conformal mapping in Complex Analysis

    I would appreciate if someone could explain Conformal Mapping using Complex Analysis using an example. I get the rough idea but have no clue how complex analysis comes into the picture. Thank You!
  47. C

    What makes 1-1 mappings special and why do we use them in mapping and functions?

    Mapping and functions... Why do were define one-one and many-one mappings as functions? Why do we separate them into a different group and make them special? Thanks in advance. :smile:
  48. BobG

    News Mapping the Global Future - 2020

    This makes for some interesting reading. http://www.foia.cia.gov/2020/2020.pdf The rise in economic power of China and India is pretty much a given. One prediction is really striking. They predict the world's economy to grow by 80 percent over 2000 levels. At that rate, the worst that...
  49. DocToxyn

    How Can I Map Cell Fate Using CRE-Based Lineage Mapping?

    I am interested in following the fate of cells in which a particular cytosolic receptor/transcription factor has been activated during development. Would something like a CRE recombinase transgenic work for this? Can anyone who worked with this system or has working knowledge of it give me a...
  50. C

    Did ancient civilizations use astronomy for scientific purposes?

    I have been speculating that the ancients believed in eternal life or re-incarnation because when you fall asleep you never actually remember the point at which you actually pass out...you just remember waking up. The ancients commonly believed certain gods had domain over natural elements...
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