My question is simple, but I cant find solid answer for this. I can make hole in face like this:  But it makes a lot of 3 polygons faces. or make hole like this:  Is it better to make holes in few seconds like on first picture with a lot of 3-gons or is it right to take time and make it like on second picture with all 4-gons? and why? I looked at some youtube videos or websites, but they make hole and dont really say anything about topology.
Support for N-Gons (polygons consisting of more than 4 vertices) has been in Blender for a while now, but many of us still may not know when to use them, and how to do so effectively.  In what situations do N-Gons really come in handy? When should they be just plain left out? Do they have any place in finished models?
change terminal title I want to make a shell alias that starts a certain program and also changes the title of the terminal to the name of the program.  How can I do that?  In case it matters, I am running the terminal on Ubuntu and connecting to a Debian server via ssh. How to run scripts without typing the full path? In a theoretical physics homework problem, I have to show the following: $$\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$$  Where $T$ is the Energy-Momentum-Tensor, $j$ the generalized current and $F$ the Field-Tensor. We use the $g$ for the metric tensor, I think in English the $\eta$ is more common.  I know the following relationships:   Current and magnetic potential with Lorenz gauge condition: $$\mathop\Box A^\mu = \mu_0 j^\mu$$ Energy-Momentum-Tensor: $$T^{\mu\nu} = \frac1{\mu_0} g^{\mu\alpha} F_{\alpha\beta} F^{\beta\nu} + \frac1{4\mu_0} g^{\mu\nu} F_{\kappa\lambda} F^{\kappa\lambda}$$ Field-Tensor: $$F^{\mu\nu} = 2 \partial^{[\mu} A^{\nu]} = \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}$$ d'Alembert operator: $$\mathop\Box = \partial_\mu \partial^\mu$$ Bianchi identity: $$\partial^{[\mu} F^{\nu\alpha]} = 0$$   So far I have set all the definitions into the formula I have to show, but I only end up a lot of terms from antisymmetrisation and product rule. I also drew all what I have in , but I still cannot see how to tackle this problem.  Could somebody please give me a hint into the right direction? After closing paint the last used settings went back to default. I want them to be saved. Like the selected Brush-Tool, Color, Line-strength, etc.  Either after every usage or I define one I use most. Maybe through the registry or by start parameters? Counting homomorphisms between $\Bbb Z$ and $\Bbb Z_n$ and also between $\Bbb Z_n$ and $\Bbb Q$ I have an exercise found on a list but I didn't know how to proceed. Please, any tips?  Let $X$ be a connected subset of a connected metric space $M$. Show that for each connected component $C$ of $M\setminus X$ that $M\setminus C$ is connected. For a graph $G$, let $W$ be the (random) vertex occupied at the ﬁrst time the random walk has visited every vertex. That is, $W$ is the last new vertex to be visited by the random walk. Prove the following remarkable fact:      For the   random walk on an $n$-cycle, $W$ is uniformly distributed over all vertices different   from the starting vertex. Using getopts to process long and short command line options When should I use a struct rather than a class in C#? When should you use struct and not class in C#? My conceptual model is that structs are used in times when the item is merely a collection of value types.  A way to logically hold them all together into a cohesive whole.  I came across these rules :   A struct should represent a single value. A struct should have a memory footprint less than 16 bytes. A struct should not be changed after creation.   Do these rules work? What does a struct mean semantically? I'm looking for the title of an anthology of children's science fiction stories from the 1950s. The best of the bunch involved a Martian who visited earth, and realized we'd blown ourselves up in a nuclear war and had fallen into savagery. The Martian is a vegetarian who subsists on biscuits made by a machine he brought with him, and communicates by using one of his tentacles to feed messages direction to/from the brain of the person he's talking to.  Inadvertently left behind by his expedition, he initially befriended some children, and eventually managed to rebuild civilization. Presently he dies, but when another expedition comes a generation later, they find the civilization he rebuilt.  there were other stories, but that was the best one.   If I can't find the name of the book it was in, I'd be happy to settle for the name of the author and the title of the story. The problem is stated as follows:  "Let $R$ be a Noetherian ring and $\theta$ be a ring homomorphism from $R$ to $R$. Show that if $\theta$ is surjective then it is also injective."  Regardless of the right solution, I don't understand why is the following wrong:     We have $\theta: R\to R$. By the isomorphism theorem $R/\ker\theta\cong\operatorname{Im}\theta$. Since $\operatorname{Im}\theta = R$, it follows $\ker\theta =0$, so it's injective.   Harsh criticism will be appreciated. Thanks. Understanding how references and labels work I'm trying to understand why I cannot effectively reference figures or equations that I have defined with labels.  For example:  \begin{figure}   \label{fig:area_Treasuries}   \caption{Treasuries as a portion of total financial flows.}   \centering   \includegraphics[width=0.75\textwidth]{graphs/Area_Treasuries.png} \end{figure}  \paragraph{} Figure~\ref{fig:area_Treasuries} presents Treasuries (both flowing into and out of the United States) as a share of total financial flows.  From 1985 to 2010, Treasuries account for, on average, 53.2\% of total financial flows.   With the above code, I get this warning:      LaTeX Warning: Reference `fig:area_Treasuries' on page 37 undefined on   input line 477.   The result is "Figure ?? presents Treasuries..."  Why is this happening?  Related, I don't understand why I can't reference, say, an equation before (I mean physically above in the text) the actual equation.  Isn't this what compiling multiple times and cross references is supposed to take care of? Find an example where Markov's inequality is tight in the following sense: For each positive integer $a$, find a non-negative random variable $X$ such that $P(X\ge a)=E(X)/a$.   How to do this problem, I am really confused. Also, what is the definition of Markov's inequality? Stability region for two step Nyström method I have the following two step Nyström method: $u_{k+1}=u_{k-1}+2h\cdot f(u_k)$. I want to know the stability region, so I wrote this as $w_{k+1} = A\cdot w_k$ with $A=\left(\begin{matrix} 2h\lambda &amp; 1 \\ 1 &amp; 0\end{matrix}\right)$ and $w_k = (u_{k},u_{k-1})^t$. I use the sample/test equation $u'=\lambda\cdot u = f(u)$ with $\lambda\in\mathbb{C}$. To find the stability region I must set some limitations on the matrix A.  Do I want the whole vector $w_{k+1}$ to go to the zero vector as $k$ goes to infinity, or just the first component that contains $u_{k+1}$? I don't think I can let the second component go to zero, since the matrix just has a $1$ in the bottomleft corner. So I think I want $2h\lambda$ to be negative in the reals (like Forward Euler) , or at least less than 1? I'm unfortunately just guessing at this point.  For (Forward) Euler we have $u_{k+1}=u_k + h\cdot f(u_k) = (1 + h\lambda)u_k$ and so we require that $h\lambda$ does not have a positive real part.  So I guess I also want some anologue for matrices being less than 1? I do not know how to deal with the matrices since the left hand vector not only contains $u_{k+1}$ but also the old $u_k$. Convert timestamps with offset to datetime obj using strptime Why are there non-visible objects in my final render? Have Blender on about 4 machines rendering animations. Just spotted on one of the machines its rendering something different from the actual scene that I have setup.    Top window shows a different set of layers objects to whats actually being rendered in the rendering window below.  In my scene contents, layers objects 1-5 are not visible, but these are the ones that look like they are being rendered.  The only thing I can assume is that perhaps it might be because I did not save the document before clicking render, but I would not have expected that behaviour (you dont need to save your word document before printing it).  Can anyone confirm why this is happening? In the sentence: "Drinking and driving IS dangerous", why does the verb "to be" need to be singular? In the sentence: "Drinking and driving is dangerous". Drinking and driving are both subjects and the word dangerous is the object (I think) but why do I have to use the verb to be in singular? How to use numpad / on a keyboard without a numpad? I've just got into Blender, and I like it a lot. But as I just switched from a stationary computer to a MacBook, I've got some new problems regarding the numpad. I can use 1-9 perfectly, But I have no idea how to emulate buttons like / (used to enter local view). I've searched the web for an answer, but I can't find any. "Hail Mary", "Glory Be" in the plural Possible Duplicate:          In the rosary, a Catholic sacramental composed of prayer beads, there is a short prayer concluding each decade called "Glory Be" ("Glory be to the Father, Son and Holy Spirit...").  Would the plural be Glory Bes or Glory Be's?  Likewise, do you say 10 Hail Marys? Consider the infinite line, $L$ in $2D$ consisting of all points $p$ such that $p.[0.3511 0.9263]= 6$. Find the point on the line closest to $(10, 20)$. Find the point on the line closest to $(4, 3)$. Find the distance from the line to both of these points.  Hi, I was reading the book $3D$ Maths Primer for Graphics and Game Development. The book mention about $2$ formulas but I don't know how to apply them.   $\text{Signed distance} = d-q.n$  $q' = q + (d-q.n)n$  for any point $q$, the point $q'$ that is the closest point on $L$ to $q$.  This is what I have tried,   Since the lines are parallel then the normal are the same so   $q' = q + (6 - q(0.3511 0.9263))(0.3511 0.9263)$   I'm stuck here.