## mesh – Manipulates MeshRegion as a normal Mathematica expression

But avoid

• Make statements based on opinions; Provide them with references or personal experience.

Use MathJax to format equations. Mathjax reference.

## delayed rendering – how to calculate normal from a normal map in space? (OpenGL)

I am trying to do normal mapping in a lagged renderer and I don't know how to implement normal maps anymore. I have a bool that tells whether a normal mapped value should be used or not, and thus whether the TBN matrix should be calculated. My vertex code for the geometry run looks like this:

#version 410 core

layout (location = 0) in vec3 aPos;
layout (location = 1) in vec3 aNormal;
layout (location = 2) in vec2 aTexCoords;
layout (location = 3) in vec3 aTangent; // Optional Texture coordinates
layout (location = 4) in vec3 aBitangent; // Optional Texture coordinates

out vec3 FragPos;
out vec2 TexCoords;
out vec3 Normal;
out mat3 TBN;

uniform mat4 model;
uniform mat4 view;
uniform mat4 projection;

uniform bool hasNormalMap;

void main()
{
vec4 worldPos = model * vec4(aPos, 1.0);
FragPos = worldPos.xyz;
TexCoords = aTexCoords;
Normal = transpose(inverse(mat3(model))) * aNormal;

if(hasNormalMap)
{
vec3 T = normalize(vec3(model * vec4(aTangent, 0.0)));
vec3 N = normalize(vec3(model * vec4(aNormal, 0.0)));
// re-orthogonalize T with respect to N
T = normalize(T - dot(T, N) * N);
// then retrieve perpendicular vector B with the cross product of T and N
vec3 B = cross(N, T);
mat3 TBN = mat3(T, B, N);
}

gl_Position = projection * view * worldPos;
}


Here I am confused:

In my calculation, I multiplied T and N by the model matrix that should have moved it into space. Now the transpose (T, B, N) should bring me back to the model space (I think I'm not sure). How can I use the TBN in the fragment shader to calculate the normals in space?

If there are better approaches, they are welcome. Thank you very much.

To update:
I removed the transposition of the TBN as there is no reason to turn into a tangent space if we want to pass it in space. How do we apply the TBN matrix in the fragment shader so that the normal lighting value is correct? I have currently done:

#version 410 core

layout (location = 0) out vec3 gPosition;
layout (location = 1) out vec3 gNormal;
layout (location = 2) out vec4 gAlbedoSpec;

in vec2 TexCoords;
in vec3 FragPos;
in vec3 Normal;
in mat3 TBN;

struct Material {
sampler2D diffuseMap;
sampler2D specularMap;
sampler2D normalMap;
float shininess;
};

uniform Material material;
uniform bool hasNormalMap;

void main()
{
// store the fragment position vector in the first gbuffer texture
gPosition = FragPos;

// also store the per-fragment normals into the gbuffer
gNormal = normalize(Normal);

if(hasNormalMap)
{
gNormal = texture(material.normalMap, TexCoords).rgb * TBN;
gNormal = normalize(gNormal);
}

// and the diffuse per-fragment color
gAlbedoSpec.rgb = texture(material.diffuseMap, TexCoords).rgb;

// store specular intensity in gAlbedoSpec's alpha component
gAlbedoSpec.a = texture(material.specularMap, TexCoords).r;
}


but it doesn't feel right. I imagine that I would transform the sampled value from the normal map through the TBN matrix to get it in space. Do I miss something?

## What is the normal order rate from VPS

What is the normal order rate of VPS | Web hosting talk

& # 39);
var sidebar_align = & # 39; right & # 39 ;;
var content_container_margin = parseInt (& # 39; 350px & # 39;);
var sidebar_width = parseInt (& # 39; 330px & # 39;);
// ->

1. ## What is the normal order rate from VPS

Hello, I run a web hosting business with my friends. Currently focuses on the sale of VPS. May I know what the normal order price for VPS is? What is the maximum order you have daily, weekly and monthly?

#### Publish permissions

• You not allowed post new topics
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• You not allowed Post attachments
• You not allowed Edit your posts

## Battery – The MacBook Pro 16 "is about 10 degrees hotter when idle. Is this normal?

This is almost certainly the case, as Apple strictly controls the heat and power sleeves when the charger is turned on and off. I would avoid delaying a return by getting a remote system scan through AppleCare and then asking if it is worth exchanging. Your MacBook Pro can run for hours and days on a CPU at or near 100 ° C. A small difference with low performance makes a lot of sense to be the basic settings for a lightly loaded system in idle.

I expect we'll soon have more control than today to both lower performance and activate earlier.

## Is there a 2-transitive finite group with a transitive normal subgroup with a cyclical quotient?

To let $$G leq S_n$$ His $$2$$-transitive. Is it possible that it exists $$N lhd G$$ With $$N$$ transitive and $$G / N$$ cyclically?

I am particularly interested in the answer when $$n$$ is big and even if the group $$G$$ is $$3$$-transitive.

## Differential geometry – How is the normal field defined on the finite union of surfaces?

To let $$M$$ a 2-dimensional be embedded $$C ^ 1$$-submanifold of $$mathbb R ^ 3$$a subset of $$mathbb R ^ 3$$ so for everyone $$x in M ​​$$ There is a two-dimensional graphic$$^ 1$$ $$(U, phi)$$ of $$M$$ With $$x in phi (U)$$, Especially for everyone $$u in U$$ and $$x: = phi (u)$$. $$N_x phi (U)$$ is one-dimensional and therefore there is a unique one $$nu _ { phi (U)} (x) in N_x phi (U)$$ the unit length with $$det left ({ rm D} phi (u), nu _ { phi (U)} ( phi (u)) right)> 0 tag2.$$ To be exact, $$nu _ { phi (U)} (x) = frac { partial_1 phi (u) times partial_2 (u)} { left | partial_1 phi (u) times partial_2 (u) right |} tag3$$ and thus the dependence on $$nu _ { phi (U)} (x)$$ on $$x$$ is continuous.

Question 1: In general, there is a countable system $$mathfrak A$$ of 2-dimensional diagrams with $$M subseteq bigcup _ {(U, : phi) in mathfrak A} phi (U)$$, Can we immediately conclude that? $$nu_M$$ by defining $$nu_M (x) = nu _ { phi (U)} (x)$$ to the $$x in M ​​$$ and $$(U, phi) in mathfrak A$$ With $$x in phi (U)$$? Is it well defined, unique and consistent?

Question 2: How can we generalize the existence of $$nu_M$$ too general $$M subseteq mathbb R ^ 3$$? I don't want to be too general, but I have to pick up the case of a cube made of six squares or a box on a table. So maybe something like that $$M$$ the finite union of "piece by piece $$C ^ 1$$"embedded $$C ^ 1$$-submanifolds $$M_i$$ "possibly with limit". However, I would need some help on how exactly "piece by piece" $$C ^ 1$$ and "with limit" must be defined here. And I wonder if we have to accept that $$M_i$$ is a closed sentence.

$$^ 1$$ i.e. $$U subseteq mathbb R ^ 2$$ is open, $$phi: U to mathbb R ^ 3$$ is an immersion and a topological embedding of $$U$$ in $$M$$ and $$Phi (U)$$ is an open subset of $$M$$ (equipped with the subspace topology).

$$^ 2$$ $$v in mathbb R ^ 3$$ is called tangent vector $$M$$ at the $$x in M ​​$$ If there is a … $$varepsilon> 0$$ and a $$gamma in C ^ 1 ((- varepsilon varepsilon), M)$$ With $$gamma (0) = x$$ and $$gamma ((0) = v$$,

## Is this language normal over 0 and 1?

The language L = {xyx, where x, y are any strings above {0,1}}.
Is this a regular language?
How can this be shown?

## Blinking, blurring, normal hiding and moving?

Exactly what the title says: blinking, blurring, normal hiding and moving? Is one of them stacking? Are all piling up? Which, if any?

## Is there an accessibility policy for the contrast of a key color between a normal state and a floating state?

I am a designer with a typical basic understanding of accessibility.

My question is that there is an access rule for the color contrast of a button that is in a normal state compared to a button that is in a floating state? I tried to look for it, but I'm out of luck. I use material design, but the color of the individual conditions does not seem to have enough contrast to each other.

## Probability – Is the expectation of $xy / (x ^ 2 + (x + y) ^ 2)$ for i.i.d. standard normal $x, y$ finally?

To let $$x, y$$ i.i.d. Standard normal random variables. Is the following expectation limited?

$$mathbb {E} Big ( frac {xy} {x ^ 2 + (x + y) ^ 2} Big)$$

I used Wolfram Alpha and Simulation to calculate the above expectation and in both cases I got the value -0.2. I am not sure if I can trust this result because the ratio distributions are often very limited.

Another thing I've observed is that, even though the ratio $$x / y$$ If the Cauchy distribution has an expectation that is not defined, Wolfram Alpha calculates the expectation $$mathbb {E} (x / y)$$ as zero.