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. foldedelephants

    How to solve restriction mapping problems?

    Homework Statement A piece of linear DNA 1000bp long is completely digested by four enzymes, E, B, P, and S. We are given the sizes of fragments (in bp) produced when each of the enzymes are used in isolation, and when they are used in different combinations: E : 227, 773 B : 150, 450, 400 P ...
  2. P

    Isoparametric Mapping Homework: Displacement, Deformation Gradients

    Homework Statement I have an initial configuration and a final configuration for a sample that has been stressed. Both of these are trapezoidal shapes and I have exact coordinates for each point. I know how to use the shape equations as well as deriving the Jacobian. Additionally I have...
  3. M

    MHB Show that the mapping is surjective

    Hey! :o I am looking at the following exercise: Let $C$ be an algebraic closure of $F$, let $f\in F[x]$ be irreducible and let $a,b\in C$ be roots of $f$. Applying the theorem: "If $E$ is an algebraic extension of $F$, $C$ is an algebraic closure of $F$, and $i$ is an embedding (that is, a...
  4. R

    MHB Finding the Matrix Associated with a Linear Mapping on a Real Matrix

    I am working on a two-by-two real matrix $M$, with a linear mapping $F$ that returns the sum of $M$ and its transpose. I need to find out the matrix that is associated with the mapping. To the best of my understanding: $$ M + M^T = \begin{bmatrix} r &s\\ t &u \end{bmatrix} + \begin{bmatrix} r...
  5. R

    MHB Proving disjoint of Kernel and Image of a linear mapping

    I am working on a problem that goes like this: Show that $Ker (F) \cap I am (F) = \{0\}$ if $F: W \rightarrow W$ is linear and if $F^4 = F.$ I have the solution but there is one step which I need help: (the delineation is mine) (1) Suppose that there exists $x$, such that $x \in Ker(F) \cap...
  6. R

    MHB How Do You Prove a Mapping is Surjective?

    I have a mapping $L: \mathbb R^3 \rightarrow \mathbb R^3$ as defined by $L(x, y, z) = (x+z, y+z, x+y).$ How do you prove that the $L$ is an onto mapping? I know for sure that $\forall x, y, z \in \mathbb R$, then $x+z, y+z, x+y \in \mathbb R$ too. Then I need to prove that $Im (L) = \mathbb...
  7. Zeeree

    Mobius transformation for the first quadrant

    Homework Statement Find the images of the following region in the z-plane onto the w-plane under the linear fractional transformations The first quadrant ##x > 0, y > 0## where ##T(z) = \frac { z -i } { z + i }## Homework EquationsThe Attempt at a Solution [/B] So for this, I looked at the...
  8. B

    A How can conformal mapping be used to convert curves between different maps?

    I know the concepts of conformal mapping and complex mapping but I didn’t see none explanation about how apply this ideia and formula for convert a curve, or a function, between different maps. Look this illustration… In the Cartesian map, I basically drew a liner function f(x) = ax+b...
  9. Mycelium

    Partial digest in restriction mapping

    Homework Statement The question: Scientists need to take precautions when they carry out restriction mapping. They need to make sure that the enzyme they have used has completely digested the DNA. One check they may carry out is to add the sizes of the fragments together. How could scientists...
  10. Deveno

    MHB De-mystifying universal mapping properties: an example-quotient groups.

    Often, in the study of algebraic objects certain things (like tensor products) are often defined primarily in terms of an universal mapping property. When one is used to "concrete objects" one can calculate with, this often comes as a shock to the system. One feels as if one is spinning...
  11. R

    Automotive Help on throttle mapping for gas/electric hybrid motor

    hey all - ive built an big amp DC electric kart, and want to add a gas motor for secondary drive. not going serial hybrid - I want both to be drive motors. I've written controller code (can link to it if anyone wants) - but the problem is not the code - its how to map the transition of...
  12. J

    I Proper mapping of the second postulate into math

    The second postulate of SR is telling us that light always travels at C in a vacuum(absent of gravity) measured by any observer independent of the source or inertial frame the observer is measuring the light from. However, light is made up of photons which do not travel like ping pong balls in...
  13. S

    Mapping a Function: Solving Homework Statement

    Homework Statement [/B] Hello all, thank you in advance for your help. Please let me know if this is the wrong forum. My problem: Let x= a + b√2 and let y= the 2 x 2 matrix {a 2b}{b a}. Show that x maps to y. Homework Equations [/B] As I see it, for multiplication, this is pretty...
  14. Strilanc

    I Mapping between rotations and operations: sign & handedness

    I have a toy quantum circuit simulator that I work on. I want to visually represent operations in multiple ways: as a Hamiltonian, as a unitary matrix, and as a Bloch sphere rotation. I want to double-check that I haven't flipped anything. I'll focus a concrete example: is this animation...
  15. Estanho

    I Symmetric injective mapping from N² to N

    Hi, I've been trying to find one symmetric "injective" N²->N function, but could not find any. The quotes are there because the function I'm trying to find is not really injective, as I need that the two arguments be interchangeable and the value remains the same. In other words, the tuple (a...
  16. C

    What is the proper notation for finding all mapped x in R4 using linear algebra?

    Homework Statement Linear algebra:[/B] Find all x in R4 space that are mapped into the zero vector for the given matrix A A= | 1 -4 7 -5 | | 0 1 -4 3| | 2 -6 6 -4|Homework Equations None... it's linear algebra. Don't ban me. The Attempt at a Solution I tried RREF on this after...
  17. E

    Good Vibration Stability Mapping Software?

    Hello Physics Forum patrons! I am currently in search for some software and maybe hardware to analyze and map vibration/stability for rotating cutting tools (CNC milling). Being primarily a machine programmer and product designer, I have a very minimal understanding of vibration from a physics...
  18. sa1988

    Prove a linear mapping of a polynomial function is a map

    Homework Statement The bane of all physicists... 'Proof' questions... So we have the mapping, Δ : P3→P3 Δ[P(x)] = (x2-1) d2P/dx2 + x dP/dx And I need to prove that this is a linear mapping Homework Equations Linear maps must satisfy: Δ[P(x+y)] = Δ[P(x)] + Δ[P(y)] and Δ[P(αx)] - αΔ[P(x)]...
  19. PsychonautQQ

    Finding a matrix to represent a 2x2 transpose mapping

    Homework Statement Let L be a mapping such that L(A) = A^t, the transpose mapping. Find a matrix representing L with respect to the standard basis [1,1,1,1] Homework EquationsThe Attempt at a Solution So should I end up getting a 4x4 matrix here? I got 1,0,0,0 for the first column, 0,0,1,0 for...
  20. PsychonautQQ

    Is the Operator D² + 2D + I Invertible on Polynomial Spaces?

    Homework Statement Let P be the vector space of one variable polynomials with complex coefficients. if D: P-->P is the derivative mapping, show that the linear mapping D^2+2D+I is invertible. Homework Equations show that D^2+2D+I is both injective and surjective The Attempt at a Solution...
  21. PhysicsKid0123

    What Is Conformal Mapping in Complex Analysis?

    "Definition: A map ƒ: A ⊂ ℂ→ ℂ is called conformal at z0, if there exists an angle θ ∈[0,2Pi) and an r > 0 such that for any curve γ(t) that is differentiable at t=0, for which γ(t)∈ A and γ(0)= z0, and that satisfies γ ' ≠0, the curve σ(t) = ƒ(γ(t)) is differentiable at t=0 and, setting u =...
  22. Jarvis323

    Optimal Color Mapping for Electric Field Visualization?

    Say you have a cross section of an electric field, and you want to make a visualization, not just of the magnitude, but showing each 3 components (negative and positive). What kind of colour transfer function scheme would you think is best in order to show the information that a physicist would...
  23. A

    Can MRI Fringe Fields be Mapped in a 3D Space?

    Hello everybody, I am working on a project that require to have map of an MRI machine fringe field in 3d space. I basic idea is to measur it in one plane parallel to radius of machine and then by assuming that field is axissymetric make my map. does anybody have any idea on doing that or on my work?
  24. O

    MHB Proving Contraction Mapping: The Linear Map $T$

    The linear map $T:{R}^{2}\to {R}^{2}$, $T(x,y)=\left(\frac{8x+8y}{10},\frac{x+y}{10}\right)$ is not a contraction with respect to the Euclidean metric, but is a contraction with respect to $d(x,y)=\sum_{i=1}^{n}\left| {x}_{i}-{y}_{i}...
  25. O

    MHB Kannan mapping and quasi-nonexpansive mapping

    Definition of Kannan Mapping Let (X,d) be a complete metric space...İf for each $x,y\in X$ following condition holds, then $T:X\to X$ is Kannan mapping $d(Tx,Ty)\le\alpha\left[d\left(x,Tx\right),d(\left(y,Ty\right)\right)]$ $\alpha\in[0,\frac{1}{2})$ Definition of Quasi-Nonexpansive...
  26. davidbenari

    Complex Mapping - Is transforming boundaries enough?

    Say I will make the transformation from the ##z## plane to the ##w## plane. Moreover, I'll transform a region ##R## with boundary ##C## in the ##z## plane to something in the ##w## plane. Why is it that if I know the equations for ##C## then I can transform these and immediately know that ##R##...
  27. O

    MHB Continuous mapping and fixed point

    Let $T$ be a continuous mapping of a complete metric space $X$ into itself such that ${T}^{k}$ is a contraction mapping of $X$ for some positive integer $k$. Then $T$ has a unique fixed point in $X$. Proof: ${T}^{k}$ has a unique fixed point $u$ in $X$ and...
  28. O

    MHB Proof of Contraction Mapping for $f\left(x\right)={e}^{{-e}^{-x}}$

    Please can you prove that $f\left(x\right)={e}^{{-e}^{-x}}$ is contraction mapping on R...Thank you for your attention...
  29. A

    Question about biology - gene mapping

    Homework Statement Homework Equations RF = (#Recombinants)/(Total offspring) x 100 The Attempt at a Solution How do I know that b is unlinked? I know that unlinked genes have a recombination frequency of 50% or higher, but how do I calculate RF for the genes here?
  30. O

    MHB Contraction and contractive mapping

    Let $(X,d)$ be a complete metric space, and suppose that $f:X \to X$ satisfies the condition: for each $\epsilon >0$, there exists $\delta > 0$ such that for all $x,y \in X$ $$ \epsilon \le d(x,y) < \epsilon+\delta \implies d(f(x),f(y)) < \epsilon.$$Clearly, this condition...
  31. RJLiberator

    Complex Analysis simple Mapping question

    Homework Statement Find the image of the rectangle with four vertices A=0, B= pi*i, C= -1+pi*i, D = -1 under the function f(z)=e^x 2. The attempt at a solution So, the graph of the original points is obvious. Now I have to map them to the new function. Seems easy enough, but I am not getting...
  32. L

    Mapping computer state changes as a space.

    I want to see if we can map the space that is computable programs. You wouldn't consider complex problems, once you mapped the simplest problems into a space of points you can get a distribution. You may see that these clump. Seeing as several of the variables are proportional to the history of...
  33. D

    Conformal Mapping: Sketch Regions & Find Mapping

    Hi, I need to sketche ach of the following regions: R = {z :|z| < √2, 7π/16 < Argz<9π/16}, R1 = {z :|z| < 16, Rez>0} and write down a one-one conformal mapping f1 from R onto R1. Here is my sketch https://onedrive.live.com/redir?resid=4cdf33ffa97631ef%2110238 But I'm finding hard to find the...
  34. N

    Complex Analysis: Open Mapping Theorem, Argument Principle

    Homework Statement In each case, state whether the assertion is true or false, and justify your answer with a proof or counterexample. (a) Let ##f## be holomorphic on an open connected set ##O\subseteq \mathcal{C}##. Let ##a\in O##. Let ##\{z_k\}## and ##\{\zeta_k\}## be two sequences...
  35. Hepth

    Integration : Mapping Smoothly (-inf, 2] to [0.1,0.9]

    I have an Integral that is convergent over the range (-inf, Lambda) where 0< Lambda < 1. I need to change variables to move this to (0.1, 0.9) in such a way that I do not introduce any poor behavior, such as asymptotes or discontinuities as it needs to be well behaved. Is there a standard...
  36. P

    Best vectors for gene mapping (FISH)?

    If you were to have clones of genes you wished to use for FISH in the form of a plasmid, cosmid, BAC and YAC, which would be best for gene mapping? I'm unsure as to what the distinction would be between these types particularly for use in FISH. Which is most commonly used and why? Thanks
  37. M

    Other Conformal Mapping: Textbook for Electrodynamics Learning

    What's a good textbook to learn conformal mapping in electrodynamics?
  38. PsychonautQQ

    Equivalence mapping from integers to rationals

    Homework Statement Let * and = be defined by a*b means a - b is an element of the integers and a = b means that a - b is an element of the rationals. Suppose there is a mapping P: (* equivalence classes over the real numbers) --> (= equivalence classes over the real numbers). show that this...
  39. C

    Mapping of the standard k-simplex in R^n to X

    My book denotes by σ:Δk→X for some suitable topological space X a standard k-simplex of X. It then describes the free abelian group generated by such σ's as the group of k-chains on X. It is not clear to me what is meant by a chain for a map σ. I understand a chain in Rn to be sums of integer...
  40. C

    Solving Mapping / Set Problems: F(x) and R = All Real Numbers | Homework Help

    Homework Statement R = all real numbers F(x) = { y in R : sin(y) = x} 1. Is F a mapping from R to R 2. Describe the three sets F(5), F(0), F(1). 3.Can F be represtented as a function from R to R 4. Give two different choices of X and Y (take both X and Y to be subsets of ?) so that F can...
  41. K

    Operator state mapping in Conformal Field Theory

    can anyone suggest any good reading material on operator state mapping in conformal field theory? I know only elementary field theory... So it might be helpful ifsomeone suggest a book where it is done in little detailed way..
  42. K

    Conformal mapping from polygon with circle segments

    I am looking for a conformal map from a "polygon" to eg the upper half plane, which consists of circle segments instead of lines. So for example, it could be a quadrilateral ABCD, but where AB is a circle segment. The closest I can find is the Schwarz-Christoffel mapping. Anyone has any tips?
  43. PcumP_Ravenclaw

    Derivation of mapping for isometric rotation about i

    Homework Statement 2. Find the formulae as in (3.4.1) for each of the following: (a) the rotation of angle π/2 about the point i ; Homework Equations The equation 3.4.1 is given below. ## f(z) → z*a + b ## where a, b and z are all complex numbersThe Attempt at a Solution I have attached my...
  44. B

    Determining when a mapping is an isomporphism

    Homework Statement Suppose that ##\phi : \mathbb{Z}_n \rightarrow \mathbb{Z}_n##, where the rule is ##\phi([a]_n) = [ka]_n##. Formulate and prove a conjecture that gives necessary and sufficient conditions on the positive integers ##k## and ##n## which would guarantee that ##\phi## is an...
  45. I

    Mapping Space with Clocks: Deduce Distances/Observers w/ Constant Light Speed

    Suppose that we do not have any way to measure distance, but do have clocks. There are N observers, who can all see the distant events, say spaceships taking off and landing on far away planets. The question is: assuming the speed of light is constant, can we deduce the distance to the events...
  46. C

    MHB Mapping an exponential curve between two points

    Hi, I'm building a fluid model and using the method of characteristics to solve it. I'll not go into the details as they aren't necessary. Basically I have two points $(-\epsilon,70)$ and $(\epsilon, 0)$ and need to create an exponential curve between them. Could someone please tell me of a way...
  47. M

    Mapping 3D point to cone surface using perpendicular line

    Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.
  48. J

    Conformal Mapping: Transforming Polygons to Circles?

    Is there a conformal mapping that transforms regular polygons (e.g. triangle and square) to circle?
  49. KleZMeR

    Conformal Mapping: Find Points of Z Plane for f(z)=-(1-z)/(1+z)

    Homework Statement With The map f(z) = -(1-z)/(1+z) where z=x+iy, and f(z) maps z onto w = u + iv plane. show for which points of the z plane this map is conformal. Homework Equations The Attempt at a Solution I have read a lot about this subject, and I think I...
  50. Math Amateur

    MHB Universal Mapping Property of a Direct Sum - Knapp Pages 60-61

    I am reading Chapter 2: Vector Spaces over \mathbb{Q}, \mathbb{R} \text{ and } \mathbb{C} of Anthony W. Knapp's book, Basic Algebra. I need some help with some issues regarding the Universal Mapping Property of direct sums of vector spaces as dealt with by Knapp of pages 60-61. I am not...
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