I was wondering what sorts of threats a company like Twitter would be prone to, as well as what vulnerabilities they may have. I already know some such as Social Engineering, Spear-phishing, Human Error, Third-Party Apps and Suppliers, Disgruntled employees, Man in the middle attacks, DDoS, so I was wondering if there are any other types of threats out there. Thanks!

# Tag: faces

## photo editing – image to 1:1 cube faces or 2:1 spheres

When uploading jpeg to Marzipano.net tool, the error returns with “Images not 1:1 cube faces or 2:1 spheres”

After googling for an online converter and using a few, the error is still the same.

Also downloaded and tried using Microsoft Image composite editor (still have it on my computer).

I just do not know how to make an image to 1:1 cube faces or 2:1 spheres.

## differential equations – Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces

I have the three dimensional Laplacian $nabla^2 T(x,y,z)=0$ representing a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either of the $z$ faces i.e. at $z=0$ (ABCD) and $z=w$ (EFGH). Rest all the faces are insulated i.e. $x=0,L$ and $y=0,l$. The following figure depicts the situation.

The boundary conditions on the lateral faces are therefore:

$$-kfrac{partial T(0,y,z)}{partial x}=-kfrac{partial T(L,y,z)}{partial x}=-kfrac{partial T(x,0,z)}{partial y}=-kfrac{partial T(x,l,z)}{partial y}=0 tag 1$$

The bc(s) on the two z-faces are robin type and of the following form:

$$frac{partial T(x,y,0)}{partial z} = p_cbigg(T(x,y,0)-e^{-b_c y/l}left(t_{ci} + frac{b_c}{l}int_0^y e^{b_c s/l}T(x,s,0)dsright)bigg) tag 2$$

$$frac{partial T(x,y,w)}{partial z} = p_hbigg(e^{-b_h x/L}left(t_{hi} + frac{b_h}{L}int_0^x e^{b_h s/L}T(x,s,w)dsright)-T(x,y,w)bigg) tag 3$$

$t_{hi}, t_{ci}, b_h, b_c, p_h, p_c, k$ are all constants $>0$.

I have two questions:

**(1)** With the insulated conditions mentioned in $(1)$ does a analytical solution exist for this system? I tired to solve this by hand but landed on a trivial solution.

**(2)** Can someone help in solving this analytically ?

I will include the codes for help:

```
tc(x_, y_) = E^(-bc* y/l)*(tci + (bc/l)*Integrate(E^(bc*s/l)*T(x, s, 0), {s, 0, y}));
bc1 = (D(T(x, y, z), z) /. z -> 0) == pc (T(x, y, 0) - tc(x, y));
th(x_, y_) = E^(-bh*x/L)*(thi + (bh/L)*Integrate(E^(bh*s/L)*T(s, y, w), {s, 0, x}));
bc2 = (D(T(x, y, z), z) /. z -> w) == ph (th(x, y) - T(x, y, w));
```

**Origins of the b.c.**$2,3$

Actual bc(s): $$frac{partial T(x,y,0)}{partial z}=p_c (T(x,y,0)-t_c) tag 4$$

$$frac{partial T(x,y,w)}{partial z}=p_h (t_h-T(x,y,w))tag 5$$

where $t_h,t_c$ are defined in the equation:

$$frac{partial t_c}{partial y}+frac{b_c}{l}(t_c-T(x,y,0))=0 tag 6$$

$$frac{partial t_h}{partial x}+frac{b_h}{L}(t_h-T(x,y,0))=0 tag 7$$

$$t_h=e^{-b_h x/L}bigg(t_{hi} + frac{b_h}{L}int_0^x e^{b_h s/L}T(x,s,w)dsbigg) tag 8$$

$$t_c=e^{-b_c y/l}bigg(t_{ci} + frac{b_c}{l}int_0^y e^{b_c s/l}T(x,s,0)dsbigg) tag 9$$

It is known that $t_h(x=0)=t_{hi}$ and $t_c(y=0)=t_{ci}$. I had solved $6,7$ using the method of integrating factors and used the given conditions to reach $8,9$ which were then substituted into the original b.c.(s) $4,5$ to reach $2,3$.

## Computational geometry: different colors for different faces of the convex hull

```
P0={0,0,0};P1={1,0,0};P2={0,1,0};P3={0,0,1};P4={1,1,1};P5={-1,-1,-1};
R[4]=ConvexHullMesh[{P0,P1,P3,P4},Frame->True,PlotRange -> Automatic,MeshCellStyle -> {{2,All}-> Opacity[.4, Red],{1,All}->Black,{0,All}->Blue}];
Show[Region[R[4], PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2},{-1.2,1.2}},
Axes-> True, ImageSize -> Large,AxesOrigin->{0,0,0},LabelStyle ->{12,Bold,Black},AxesLabel->{x,y,z},AxesStyle->Thick,Boxed->True]]
```

I have the following 3D convex helmet. How can I give different colors to different faces of the convex helmet?

Thank you

## What has 8 faces but can't see?

it has 8 faces but can not see 412068657861676f6e616c20707269736d21204f6b2c207468617420776173206e6f742066756e6e792e20416e79776179732c206865726520697320796f757220666c61673a0a46537b65696768745f657965735f776f756c645f62655f615f626c696e645f7370696465725f3536343131427d

the suggestions are 1. What does that character set look like?

2. xxd is your friend (not xkcd although that comic strip is amazing).

## Statistics – Probability of observing at least $ k $ faces if coins have different probabilities of faces?

I have an interesting problem I have a Bernoulli motorhome collection $ {X_1, ldots, X_N } $ and know the probabilities of success of each one: $ {p_1, ldots, p_N } $.

Is there, in general, a way to efficiently calculate the probability of observing at least $ K $ successes without enumerating possible results?

## unit: I have no idea how to calculate the faces of my mesh generated by programming

So I am doing a cave program that generates programs and I have all the vertices, but I have no idea how to solve the faces of my mesh. My code:

```
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class MapGen : MonoBehaviour
{
Mesh mesh;
int() triangles;
public int xSize = 20;
public int zSize = 20;
public int ySize = 20;
(Range(0f, 4.5f))
public float SurfaceLevel = 3.5f;
Vector3() interest;
Vector3 old = new Vector3(0, 0, 0);
public bool ShowAlg = false;
(Header("Slows down the scene veiw dramaticly when in play mode!"))
public bool ShowVert = true;
// Start is called before the first frame update
void Start()
{
mesh = new Mesh();
GetComponent
```().mesh = mesh;
CreateShape();
SolveFaces();
UpdateMesh();
}
void CreateShape()
{
interest = new Vector3((xSize + 1) * (zSize + 1) * (ySize + 1));
float seed = Random.Range(0.2f, 0.5f);
Debug.Log(seed);
for (int x = 0; x <= ySize; x++)
{
for (int i = 0, y = 0; y <= zSize; y++)
{
for (int z = 0; z <= xSize; z++)
{
float ypn = (Mathf.PerlinNoise(x * seed, z * seed) * 2f);
float xpn = (Mathf.PerlinNoise(y * seed, z * seed) * 2f);
float zpn = (Mathf.PerlinNoise(x * seed, y * seed) * 2f);
if (ypn + xpn + zpn >= SurfaceLevel)
{
interest(i) = new Vector3(x, y, z);
}
i++;
}
}
}
}
void SolveFaces()
{
triangles = new int(xSize * ySize * zSize * 9);
}
void UpdateMesh()
{
mesh.Clear();
mesh.vertices = interest;
mesh.triangles = triangles;
mesh.RecalculateNormals();
MeshCollider meshc = gameObject.AddComponent(typeof(MeshCollider)) as MeshCollider;
meshc.sharedMesh = mesh;
}
private void OnDrawGizmos()
{
if (interest == null)
return;
for (int i = 0; i < interest.Length; i++)
{
if (ShowVert == true)
{
Gizmos.color = new Color (0.286f, 0.486f, 0.812f);
Gizmos.DrawSphere(interest(i), 0.2f);
}
if(ShowAlg == true)
{
Gizmos.color = Color.green;
Gizmos.DrawLine(old, interest(i));
old = interest(i);
}
}
}
}

This script is placed on an empty game object with a mesh filter, a renderer and a collider.

Keep in mind that they do nothing without faces.

I set it up so that the face array goes to `triangles`

variable and missing part of the script should go in the `SolveFaces()`

function. Thanks in advance.

## procedure generation: why does this script that eliminates duplicate faces of voxel-generated mesh not work?

Hi, this is my first post here. I am trying to do a voxel world generation project for personal experiences like Minecraft as games. But I can't find out why my script doesn't work as intended after I tried to implement a system to eliminate unnecessary faces when faced with each other. The problem is that although the script identifies that there is a neighboring block and that no face should be generated, I still get the faces in the mesh.

This is the code:

```
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
/*
*0 = front
*1 = right
*2 = back
*3 = left
*4 = up
*5 = down*/
public class ProceduralGen : MonoBehaviour
{
//The chunk game object that stores the chunk's mesh. Atm i don't have infinite chunks as to keep things simpler till the basic script is done to move to the infinite chunk gen
GameObject Chunk;
//Array that stores the block's pos and other future data.
Block(,,) blocks;
//Current Chunks dimentions, the intended number would be 256 blocks of height but i'm keeping it small for performance and simplicity sake
public int width = 10, height = 10, depth = 10;
//A float that devides the coordinates on the world space in to a float between 0 and 1 so it fits the Mathf.Perlingnoise parameters
public float res = 10f;
//Mesh data
List
``` vertices;
List triangles;
//Just a material to help view the generated Mesh
public Material material;
//This is an offset pos to help put the chunk at what a ever center i want
public Vector3 offSetPos = new Vector3(0.5f, 0.5f, 0.5f);
void Start()
{
BlockData.offSetPos = offSetPos;
blocks = new Block(width, height, depth);
Chunk = new GameObject("Cube", typeof(MeshFilter), typeof(MeshRenderer)); //setting the chunk gameobject
vertices = new List();
triangles = new List();
//Starting to generate the chunk this will be put in a separated function in the future
for (int z = 0; z < width; z++)
{
for (int x = 0; x < width; x++)
{
int y = GetHeight(x, z); // set the surface current block height based on perling noise
MakeBlock(new Vector3Int(x, y, z));
}
}
Chunk.GetComponent().material = material;
}
void MakeBlock(Vector3Int pos)
{
//Goes through a list of pre set vertices that defines how a block is made and makes a face and adds it's vertices to the vertices List
for (int i = 0; i < 6; i++)
{
//Checks if there is a block at this face's direction or it's neighbour and makes the face but here is where it doesn't work anymore
//despite the script point out there is a neighbour and it skipping the make face for this direction of the cube it still makes the face for some reason...
if (!IsBlockAt(pos, i))
MakeFace(pos, i);
}
UpdateMesh();
}
void MakeFace(Vector3Int pos, int dir)
{
//goes through each vertex inside the base cube vertices on BlockData and adds it to vertices array as well as triangulate those vertices based on an offset of vertices count - 4
for (int i = 0; i < 6; i++)
{
vertices.AddRange(BlockData.FaceVertices(i, pos));
int offSet = vertices.Count - 4;
triangles.Add(offSet + 0);
triangles.Add(offSet + 1);
triangles.Add(offSet + 2);
triangles.Add(offSet + 0);
triangles.Add(offSet + 2);
triangles.Add(offSet + 3);
}
}
bool IsBlockAt(Vector3Int pos, int dir)
{
// position helper ints that set's latter the position of the neighbour based on the direction the current face faces
int x = pos.x, y = pos.y, z = pos.z;
//setting the coordinates of the neighbour cube based on the direction
if (dir == 0)
z += 1;
if (dir == 1)
x += 1;
if (dir == 2)
z -= 1;
if (dir == 3)
x -= 1;
if (dir == 4)
y += 1;
if (dir == 5)
y -= 1;
//Checks based on perling noise if there is supose to be a block in the
neighbour's coordinate, returns true if it's not air
if (!(GetBlockAt(x, y, z) is Air))
return true;
//returns false if the last check was an air block
return false;
}
int GetHeight(int x, int z)
{
//return perling noise height times the max height of the chunk based on
the block's coordinate devided by the resolution
return (int)(Mathf.PerlinNoise((float)(x / res), (float)(z / res)) * height);
}
Block GetBlockAt(int x, int y, int z)
{
//Checks if the current block's height is lower then or the same as the perling noise at it's position if so there is a block if not there isn't
if (GetHeight(x, z) <= y)
return new Stone();
else
return new Air();
}
void UpdateMesh()
{
//Updates the mesh
Mesh mesh = Chunk.GetComponent().mesh;
mesh.vertices = vertices.ToArray();
mesh.triangles = triangles.ToArray();
mesh.RecalculateNormals();
}
}

If necessary, I can put the other scripts in this post, but I don't think it's necessary.

PS: Sorry for my bad English and bad spelling of words.

## probability: simplification of the expression for the expected number of coin tosses to get $ h $ faces in a row

$ p $ It is the probability of getting a head.

So, the expected number of coin toss before $ h $ Consecutive heads for the first time is:

$ E (x) = hp ^ h + (1-p) (E (x) +1) + p (1-p) (E (x) +2) + p ^ 2 (1-p) (E ( x) +3) + … + p h-1 (1-p) (E (x) + h) $

$ E (x) = hp ^ h + (1-p) sum_ {i = 0} h-1} p ^ i (E (x) + i + 1) $ ——–> (2)

$ E (x) = (1-p ^ h) E (x) + sum_ {i = 0} h-1} p ^ i $ ——–> (3)

$ E (x) = (1-p ^ h) E (x) + frac {1-p ^ h} {1-p} $ ——–> (4)

$ E (x) = frac {1-p ^ h} {p ^ h (1-p)} $ ——–> (5)

I got this from the answer here. I don't understand how we get expression 3 from expression 2. Can anyone explain that?

## Postprocessing: how to sew faces of different photos

Taking group photos of children is often a useless exercise. It is almost impossible to make all children look at the camera, with their eyes open and a beautiful smile on their faces.

If I take several photos in rapid succession, is there an application that can choose different faces of different photos and automatically join them into a single perfect image?