Vector calculation: Including temporary Z

I am not sure if the name of the question is sufficient.

My question is this:

I have a code that lets a camera rotate around an object (the player's name is "hero").

                Quaternion nNewRotation = Quaternion.Euler (_CameraDefaultPos.y, _Orbit_CurrentYaw, 0);

Vector3 vCurHero = new Vector3 (_HeroPos.x, _HeroPos.y, _HeroPos.z);
Vector3 negDistance = new Vector3 (_CameraDefaultPos.x, fUpDownPosition, _CameraDefaultPos.z); // fUpDownPosition was previously calculated from "Mouse Y"

Vector3 nNewPosition = nNewRotation * negDistance + vCurHero;
Vector3 nNewRotationVector = new Vector3 (_Orbit_CurrentPitch, nNewewotation.eulerAngles.y, nNewewotation.eulerAngles.z);

nNewRotation = Quaternion.Euler (nNewewotationVector);

_camera.transform.localRotation = nNewewotation;
_camera.transform.localPosition = nNewPosition;

This code works fine.

Now there is a situation where the hero changes from target to orbit.

While aiming, the camera enlarged the model. This means that the camera's local z position was -0.6f instead of -0.8f ("_CameraDefaultPos.z"), for example.

When transitioning from target to orbit, the camera's local Z position is smoothly returned to the default Z position.

I tried to include the fact that the camera may only change its z position, but all my attempts resulted in an unwanted camera position.

The next time I could get something:

                Vector3 vCurHero = new Vector3 (_HeroPos.x, _HeroPos.y, _HeroPos.z + (_CameraDefaultPos.z - _camera.transform.localPosition.z));
Vector3 negDistance = new Vector3 (_CameraDefaultPos.x, fUpDownPosition, _CameraDefaultPos.z);

But the camera is really shaky.

Does anyone know where my calculation is wrong?

Many Thanks!

Graphics – How to plot the moving position of a particle with a given time vector in Matlab?

I try to create an animation with vector in Matlab $ X $vector $ Y $ and given time vector $ T $, There are several examples of random-time animations and plots with & # 39; pause (t) & # 39 ;. It's easy with & pause (t) & # 39; to draw.

But I need a posable position $ (x, y) $ in due time $ t $,
Suppose a particle position is given by; $ X =[1,2,2]$, $ Y =[2,2,3]$ and $ T =[1,1.5,2.33]$ that is, the particle is on a coordinate (1,2) $ at the $ 1 $ secondly (2,2) $ at the $ 1.5 $ Second and further (2,3) $ at the $ 2.33 second.

I have data of this kind. I need a moving diagram of a particle in the appropriate time.

Graph Theory – Monotone Fiedler Vector

To let $ u_0 geq u_1 geq cdots geq u_ {n-1} $ be positive numbers and define a matrix $ n times n $ by $ M_ {i, j} = u _ { left | i-j right |} $ for all $ i, j $,

To let $ L = D – M $ Let be the Laplace matrix of $ M $, from where $ D $ is a diagonal matrix, so that $ D_ {ii} = sum_j M_ {i, j} $ for all $ i $, If $ lambda_1 = 0 leq lambda_2 leq cdots leq lambda_n $ are the eigenvalues ​​of $ L $, Then we can show that $ lambda_2 $ has a monotone eigenvector, called fiddler vector.

(for the proof see for example https://arxiv.org/abs/1411.0210).

When we sit down $ L & # 39; = I – D ^ {- 1/2} MD ^ {- 1/2} $ Is it possible to achieve the same result? That is, there is a monotone eigenvector $ v & # 39; $ corresponding to the second smallest eigenvalue of $ L & # 39; $?

Real analysis – Good UPPER bounds on $ log ( sum_ {i = 1} ^ n p_ie ^ {z_i}) – sum_ {i = 1} ^ np_iz_i $ where $ (p_i) _i $ is a probability vector

To let $ x = (x_1, ldots, x_n) $ be a real vector and $ (p_1, ldots, p_n) $ be a probability vector.

$ log ( sum_ {i = 1} ^ n p_ie ^ {z_i}) – sum_ {i = 1} ^ np_iz_i le ???

This paper allows us to set things like caps $ f ( sum_ {i} x_i p_i) – sum_i f (p_ix_i) $and thus a kind of reverse Jensen's inequality.

Measure theory – ODE with a measurable vector field

Suppose we have a finite measurable vector field from Borel $ F: mathbb {R} ^ n to mathbb {R} ^ n $, To avoid making the question trivial, accept this $ F neq 0 $ all over

Question. Is there at least one Lipschitz integral curve? This is a Lipschitz function $ varphi: (a, b) an mathbb {R} ^ n $ so that
$ varphi # (t) = F ( varphi (t)) $ for almost everyone $ t in (a, b) $,

This question refers to:
Set of integral curves of a vector field.

at.algebraic topology – Example of a finite group $ G $ with low-dimensional cohomology that is not generated by boot-whitney classes of flat vector bundles over $ BG $

In Stiefel-Whitney classes of real representations of finite groups, J. Algebra 126 (1989), no. 2, 327-347, Gunawardena, Kahn and Thomas addressed the question of whether cohomology is ringing $ H ^ * (G, mathbb {Z} / 2) $ was generated as an abelian group in the boot-Whitney classes of flat vector bundles over BG.

The result is that the cohomology ring of a family of cleaved metacyclic groups
$$ G_ {m, n} ^ {+} = langle t, s midt ^ {2 ^ m + 1} = s ^ {2 ^ n} = 1, , sts ^ {- 1} = t ^ {{2 ^ m} +1} rangle $$

with the property of having a card on $ D_ {2 ^ m} $ has the subgroup $ langle t rangle $ in the kernel for the targeted choice of parameters $ 1 + m-n neq m $ has a third cohomology class that is not the boot-whitney class of a vector bundle.

Are there any examples of finite groups where the second and the first cohomology group are not generated by Stiefel-Whitney classes?

App Windows – VeryPDF DWG to Vector Converter 2.0 | NulledTeam UnderGround

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Recommend Link Hight Speed | Please say Many Thanks Keep the topic live

Linear algebra – Properties of vector combinations in non-negative orthantenna

Given a vector $ x in mathbb {R} ^ {n} _ {0 +} $ so that $ x = sum ^ {k} _ {i = 1} alpha_ {i} v_ {i} $the vectors $ (v_ {1}, …, v_ {k}) in mathbb {R} ^ {n} _ {0 +} $ are an independent sentence, $ k <n $, and $ alpha_ {i}> 0 $can be seen by simple combinatorial reasoning that for at least one vector $ v_ {i} $, $ frac {|| x – alpha_ {i} v_ {i} || _ {2}} {|| x || _ {2}} geq frac {1} {k} $ (Assuming the opposite, then we have the maximum value of $ frac {|| x – alpha_ {i} v_ {i} || _ {2}} {|| x || _ {2}} < frac {1} {k} $ but that implies that $ || x – sum ^ {k} _ {i = 1} alpha_ {i} v_ {i} || _ {2}> 0 $ that is a contradiction).

Suppose we have an additional vector $ y in mathbb {R} ^ {n} _ {0 +} $ so that $ (v_ {1}, …, v_ {k}, y) $ is an independent set. What can one say? $ frac {|| x – beta y || _ {2}} {|| x || _ {2}} $ from where $ beta $ is the result of minimization $ || x-y beta || _ {2} $ be subject to $ beta geq 0 $? If $ (v_ {1}, …, v_ {k}, y) $ When set orthogonally, it seems easy to show that $ frac {|| x – beta y || _ {2}} {|| x || _ {2}} < frac {1} {k} $ (stronger statements, though I did not do the arithmetic for them, so they are not included here if I turn out to be wrong). However, the analogous statement in the absence of orthogonality does not seem so obvious. If we impose the additional requirement $ x – y beta geq 0 $ Are there more elementary conclusions that can be drawn?

P.S.
If the title I chose for this question is not exactly what I asked, I could not determine if there is a common technical term for this kind of question.

fa.functional analysis – The dual space of continuous sections in a vector bundle

If $ X $ is a compact Hausdorff space, one can view the space of complex, continuous functions as the space of connected sections in the trivial Hermitian bundle $ X times mathbb C $, According to the Riesz-Markov theorem, twice that space is the space of complex, regular Borel measures $ X $,

If $ (E, h) to X $ is a topological Hermitian vector bundle $ X $, of finite rank and if $ Gamma (X, E) $ is the space of the continuous sections equipped with the norm $ | s | = sup _ {x in X} sqrt {h_x big (s (x), s (x) big)} $, from where $ h_x $ is the Hermitian product in $ E_x $ (the fiber over $ x in X $)

does the topological dual of $ Gamma (X, E) $ have a similar nice description?

It is assumed that the bundle is locally trivial and if $ X $ If paracompact, one can try to answer the question locally, and then glue the results to a division of the unit. The answer is, however Really ugly and seems to depend in particular on the non-canonical choice of a division of unity. I'm looking for something deeper than that.

C ++, data type for storing the size of a vector

Hey, I am learning C ++ and already had experience with Python. This question is about data types, and I'm having some trouble understanding something because you do not have to declare types in Python that are specific like C ++: P

// Anyway, here's the sample code in the book
Typedef vector:: size_type vec_sz;
vec_sz size = homework.size ();

The purpose of this code is to name a type named vec_sz as the predecessor and assign the variable as type vec_sz, which stores the size of a vector called "homework." Homework is a list of positive integers.

For me, this code seems a bit over the top. Why can not we just use Int Type or Double?

The author mentions the reason for using this code, as this type guarantees for very large vector / list sizes.

So much information is greatly appreciated. cheers