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How do I determine if i just calculated the normal in the correct direction?

To explain the context, I procedurally generate buildings on unity in C#. I create a mesh and fill in the vertices and triangles, then I calculate the normals of the different points. I have several hundreds of buildings that are generated, but some faces are not in the right direction, the normals point inwards instead of outwards.
The normals are good
The normals are bad
To calculate the normals I create a Plane with the different vertex that make up the triangle, and then I retrieve the normal of the Plane. I also tested the cross product that gives the same result.
Plane plane = new Plane(v1, v2, v3);
normals.Add(plane.normal);
How i generate Triangle ?
Ex: I make a for loop on the points at the base of the building.
vectors.Add(v1);
vectors.Add(v2);
vectors.Add(v3); //v3 = v1+height
vectors.Add(v4); //v4 = v2+height
// index values
int idx1, idx2, idx3, idx4;
idx4 = vectors.Count - 1;
idx3 = vectors.Count - 2;
idx2 = vectors.Count - 3;
idx1 = vectors.Count - 4;
// Triangle 1
indices.Add(idx1);
indices.Add(idx3);
indices.Add(idx2);
...
mesh.triangles = indices.ToArray();
So my question is: How to determine if the normal is in the right direction (inside or outside)? If I can determine that, I can then flip the normal and normally it will work.

I do not totally understand your question, but for simple shapes a simple algorithm is ..
just take the "center" of the object (the CG is fine) and make a vector from there to your vertex or triangle. That direction is "outside". If you're pointing over 90° away from that, you're pointing in to the guts of the object
the next more complicated approach ...
move along your normal say "one meter". call that point "test point". you should now be "outside" your building, correct?
now you just need to check if testPoint is inside or outside your 3D shape.
in short, to determine if you are inside or outside a 3D object, you just cast a ray and count how many times you intersect with the walls. if odd, you're inside, if even you're outside.
You can google hundreds of discussions on this on the www, example https://stackoverflow.com/a/63572837/294884
Note that there are many, many variations on this, and many problems too. In some cases you start from "just inside" your normal (ie go backwards a little); sometimes it's better to start from the middle of the object (if such a thing is knowable); sometimes there are issues about how the ray casting system works in edge cases (like "right on" the surface, which is what your vertex is)
the first solution seems to me to be the right one
It may be. Sometimes it is useless. It depends on the nature of your shapes.
I wanted to avoid having to do raycast ..
Can assure you - you will have to constantly raycast during any construction process! If you wish to "avoid" casting, set the idea aside. You will be casting until you are sick of it :)
I wanted to avoid having to do raycast to limit the generation time
The good news is this is totally incorrect. Casting is extremely trivial and a very minor burden compared to everything going on in a 3D scene. When you play any 3D scene, casts are being made 100s and 1000s of times each frame.
but if I have two buildings that are close to each other, the ray will find the wall but from the second building so I couldn't determine the normal is "inside" or "outside", right?
TBC in the simple system I described. You would certainly ONLY cast against that same building that you are working on! So that's the way to go.
But indeed, unrelated to what you're asking about. Say you're in a "city". You can indeed cast through "all walls" and the parity (ie: odd or even) will let you know if you are indoors or out. This has problems though, relating to edges, corners etc. But in some case it is relevant to that problem.
As mentioned on this answer https://stackoverflow.com/a/63593282/294884 ultimately you can investigate convex hulls and more. It's a big topic!
Note that often when you build dynamic buildings/shapes, you havce a data structure of each "wall" and indeed it knows which side is in and which side out. When you do that first, it's then easy to draw the triangles the correct way. It's a big topic!

Creating Custom Convex Hull & Mesh in Unity

I'm currently trying to implement a complex search field into a unity project I'm working on, where a user has the ability to spawn points into a scene. My goal is to create a custom shape for that user based on the points they created, and then I'd like to detect whether or not other objects are inside that shape, similar to the detection of a point inside a complex hull (still shaky on the theory behind that, but an example can be found here). If possible, I'd also like the shape to update itself if the points are later moved, giving it an almost elastic, stretchy feel.
So far, every tutorial or resource I've found online does the exact same basic example, where a script assigns new verts, UVs and triangles to a custom mesh to make a plane using two triangles, but this is frustratingly simple, and decidedly unhelpful when I simply don't know what the final shape will look like, or what triangles to actually draw even when the user has as little as five points in the scene.
As of right now, the closest visual representation I could come up with has a List keep track of the user's points, and a script that just draws a bunch of pseudo-triangles using LineRenderers to connect every point, even ones that aren't exterior faces, by iterating through the List multiple times. While this looks close to what I want, it isn't actually useful in any way, as I don't know how to 'fill' those faces, and I'm still relatively lost when it comes to whether or not an object is inside that hull, like the red sphere shown in the example below.
I can also destroy and redraw those lines repeatedly during the Update() method, which allows me to grab a point and move it around, resulting in the shape dynamically changing, but this results in an undesirable flashing effect that I'd sooner avoid for now.
As this is such a broad question, I've also included the method I'm using to draw these lines below, which parents a bunch of lines shaped like triangles to an empty game object for easy destruction and recreation:
void drawHull()
{
if (!GameObject.Find("hullHold"))
{
hullHold = new GameObject();
hullHold.name = "hullHold";
}
foreach(GameObject point in points)
{
for (int i = points.IndexOf(point); i < points.Count - 2; i++)
{
lineEdge = Instantiate(lineReference);
lineEdge.name = "Triangle" + i;
lineEdge.GetComponent<LineRenderer>().startColor = Color.black;
lineEdge.GetComponent<LineRenderer>().endColor = Color.black;
lineEdge.GetComponent<LineRenderer>().positionCount = 3;
lineEdge.GetComponent<LineRenderer>().SetPosition(0, points[points.IndexOf(point)].transform.position);
lineEdge.GetComponent<LineRenderer>().SetPosition(1, points[i + 1].transform.position);
lineEdge.GetComponent<LineRenderer>().SetPosition(2, points[i + 2].transform.position);
lineEdge.GetComponent<LineRenderer>().loop = true;
lineEdge.SetActive(true);
lineEdge.transform.SetParent(hullHold.transform);
}
}
}
If anyone has encountered a similar problem somewhere else that I simply couldn't find, please let me know! Anything from more knowledge on creating a custom mesh to a more in depth and beginner-friendly explanation on determining if a point is inside a convex hull would be quite helpful. If it's at all relevant, I am working in VR and running version 2018.2.6f1 to ensure that the Oculus rift package and Unity play nice, but I haven't been having any issues working in an environment a few months behind.
Thanks!

You do mention assinging verts and tris to a mesh - this is the 'right' way to do it in unity, as it ties in with highly optimized MeshRenderer, and also I believe Colliders are able to use meshes where given the shapes like that, so you should be able to just plug into PhysX and query it for colliders overlaping with your mesh. Doing it by hand, aka iterating through faces and establishing actual bounds of your object is actually pretty hard to do effectively

How to randomly place objects as player move around in an infinity map without overlap?

I trying to make a game where player only move forward in an infinity map, and the path (just thing of them like points, the path is only the visual) is procedurally generated. I want those path to have different length (something like the tree of life, but only branches of the selected path are generated).
This is how I generate branches without overlap:
List<Vector3> everyPos; //predetermined position
public void Spawn(int amount)
{
List<Vector3> possiblePos = new List<Vector3>(everyPos);
for (int i = 0; i < amount; i++)
{
int index = Random(0, possiblePos.Count); //Find a random position
SpawnObjectAt(currentPosition+possiblePos[index]));//Create a point there
possiblePos.RemoveAt(index); //Remove that position from the list
}
}
The problem is , look at this image(I can't embed image yet):
Red is where player start, green is possible spawn position in the first move.
If there are 2 point spawned at 1 and 2, player choose point1, then the possible position in the second time will be a point in the black zone, which include point2, so if I keep continue there will eventually overlap.
How can I avoid this? I'm making a mobile game so I don't want to cache every single point. Any help would be really appreciated! Thanks!
This is a small web game that have somewhat similar mechanic to what I trying to achieve: newgrounds.com/portal/view/592325/

This is an attempt here to answer, but honestly, you need to provide more information.
Depending on the language you are writing in, you can handle this differently. You may need dynamic allocation, but for now lets assume, since your idea is quite small, that you can just do one large array predefined before compile time.
I assume you know how to make an array, so create one with say, 500 length to start. If you want to 'generate' a link like they did in that game, you simply need a random function, (there is a built in library in pretty much every language I think) and you need to do a little math.
Whatever language you use will surely have a built in graphics library, or you can use a popular easy to use one. I'll just draw a picture to make this clear.
There are a number of ways you can do this mathematically as shown in the image, using angles for example, the simplest way, however, is just to follow the boxes.
If you have worked with graphics before, you know what a vector is, if not, you will need to learn. The 9 vectors presented in this image (0,1) (1,0) (1,1) etc. can be created as vector objects, or even stored as individual ints.
To make your nodes 'move' into another path, you can simply do a rand 1-9 and then correlated the result to one of 9 possible vectors, and then add them to your position vector. It is easiest to do this in array and just use the rand int as the index. In most c derived languages you do that like this:
positionVector += changeVectorArray[rand(1,9)];
You then increment your position vector by one of the 9 vectors as shown above.
The simplest way of making the 'path' is to copy the position before you add the change vector, and then store all of the changes sequentially in another 'path' array.
To show the path on screen, simply draw a line between the first and second, second and third, third and forth elements of your path array. This formula (of joining lines) is discrete mathematics if I'm not mistaken, and you can do much more complicated path shapes if you want, but you get the gist.
That should at least start you off. Without more info I can't really help you.
I could go off on a tangent describe a bunch of different ways you can make this happen differently but its probably easier if you just ask for specifics.
EDIT>>>
Continuing with this answer, yes, looking at it now, the nodes can definitely overlap. To solve this problem you could use collision detection, every time you generate a new 'position', before adding it and drawing the line you have to loop through your array like this:
boolean copy = true;
for(int i = 0; i < getLength(pathArray); i++){
if( newVector == pathArray[i]){
copy=false;
}
}
Then of course, if copy still is true, copy the new position int the pathArray. NOTE: this whole solution is sloppy as hell, and as your array gets larger, your program is going to take longer and longer to search through that loop. This may not also guarantee that the path goes in one direction, but it is likely. And note that the lines will still be able to overlap each other, even though the position vectors can't be on top of one another.
All this considered, I think it will work, the optimization is up to you. I would suggest that there is probably a much more efficient solution using a discrete formula. You can also use such a formula to make the path go in particular directions and do other more complicated things.
You could also quite easily apply constraints on your random rolls if you want to make the path go in a particular direction. But there are so many ways of doing this I can't begin to explain. You could google path-finding algorithms for that.
Good luck.

Truncated Icosahedron Tile Objects

I'm trying to make a truncated icosahedron, though with more subdivision (so more hexagons)
In the game I use it, eacht pentagon and hexagon is a separate object. So after generating the icosahedron, I just use the generated points to place either a pentagon or a hexagon on it (instead of doing the find-middles-of-each-triangle-thing, I do this since I need them to be separate object anyway.) I have some questions about it though, and google doesn't really help, so I'm hoping there are some smart smath-knowing people here :D
Here we go:
Am I assured that the length of each sides is equal?
Since each hexa/petagon is a separate object, I need to rotate them to get them positioned properly, any help with this?
Assuming I have hexa/petagons with a radius of 1 (one), how far for the middle do I have to position them? (Basecly, whats the relationship between the radius of my hexa/pentagons and the radius of my truncated icosahedron.)
Here's my first test, I generated a icosahedron and then on each point put a pentagon model, which I rotate so it's pointing away from the middle. As you can see they still need to be rotated to fit together (question 2) and their distance to the middle has to the tweaked aswell (question 3).
I'll continue on working on this too, though all help will be appreciated! (I'm making this in Unity, using c#, so if you give sample code, it would be really really awesome if you use that.)
Thanks a lot!

Well, not the answer to your questions but maybe worth thinking about:
Wouldn't it be easier to start with a ready made Blender, Maya, ... model of a soccer ball like for example this one on Blend Swap, change it to fit your needs. Or do it on your own as there are a couple of YouTube tutorials. Then you will have far more options like LOD, materials. You can design it in Blender with each pentagon/hexagon as single object and so it will be imported in Unity.

Optimising movement on hex grid

I am making a turn based hex-grid game. The player selects units and moves them across the hex grid. Each tile in the grid is of a particular terrain type (eg desert, hills, mountains, etc) and each unit type has different abilities when it comes to moving over the terrain (e.g. some can move over mountains easily, some with difficulty and some not at all).
Each unit has a movement value and each tile takes a certain amount of movement based on its terrain type and the unit type. E.g it costs a tank 1 to move over desert, 4 over swamp and cant move at all over mountains. Where as a flying unit moves over everything at a cost of 1.
The issue I have is that when a unit is selected, I want to highlight an area around it showing where it can move, this means working out all the possible paths through the surrounding hexes, how much movement each path will take and lighting up the tiles based on that information.
I got this working with a recursive function and found it took too long to calculate, I moved the function into a thread so that it didn't block the game but still it takes around 2 seconds for the thread to calculate the moveable area for a unit with a move of 8.
Its over a million recursions which obviously is problematic.
I'm wondering if anyone has an clever ideas on how I can optimize this problem.
Here's the recursive function I'm currently using (its C# btw):
private void CalcMoveGridRecursive(int nCenterIndex, int nMoveRemaining)
{
//List of the 6 tiles adjacent to the center tile
int[] anAdjacentTiles = m_ThreadData.m_aHexData[nCenterIndex].m_anAdjacentTiles;
foreach(int tileIndex in anAdjacentTiles)
{
//make sure this adjacent tile exists
if(tileIndex == -1)
continue;
//How much would it cost the unit to move onto this adjacent tile
int nMoveCost = m_ThreadData.m_anTerrainMoveCost[(int)m_ThreadData.m_aHexData[tileIndex].m_eTileType];
if(nMoveCost != -1 && nMoveCost <= nMoveRemaining)
{
//Make sure the adjacent tile isnt already in our list.
if(!m_ThreadData.m_lPassableTiles.Contains(tileIndex))
m_ThreadData.m_lPassableTiles.Add(tileIndex);
//Now check the 6 tiles surrounding the adjacent tile we just checked (it becomes the new center).
CalcMoveGridRecursive(tileIndex, nMoveRemaining - nMoveCost);
}
}
}
At the end of the recursion, m_lPassableTiles contains a list of the indexes of all the tiles that the unit can possibly reach and they are made to glow.
This all works, it just takes too long. Does anyone know a better approach to this?

As you know, with recursive functions you want to make the problem as simple as possible. This still looks like it's trying to bite off too much at once. A couple thoughts:
Try using a HashSet structure to store m_lPassableTiles? You could avoid that Contains condition this way, which is generally an expensive operation.
I haven't tested the logic of this in my head too thoroughly, but could you set a base case before the foreach loop? Namely, that nMoveRemaining == 0?
Without knowing how your program is designed internally, I would expect m_anAdjacentTiles to contain only existing tiles anyway, so you could eliminate that check (tileIndex == -1). Not a huge performance boost, but makes your code simpler.
By the way, I think games which do this, like Civilization V, only calculate movement costs as the user suggests intention to move the unit to a certain spot. In other words, you choose a tile, and it shows how many moves it will take. This is a much more efficient operation.
Of course, when you move a unit, surrounding land is revealed -- but I think it only reveals land as far as the unit can move in one "turn," then more is revealed as it moves. If you choose to move several turns into unknown territory, you better watch it carefully or take it one turn at a time. :)
(Later...)
... wait, a million recursions? Yeah, I suppose that's the right math: 6^8 (8 being the movements available) -- but is your grid really that large? 1000x1000? How many tiles away can that unit actually traverse? Maybe 4 or 5 on average in any given direction, assuming different terrain types?
Correct me if I'm wrong (as I don't know your underlying design), but I think there's some overlap going on... major overlap. It's checking adjacent tiles of adjacent tiles already checked. I think the only thing saving you from infinite recursion is checking the moves remaining.
When a tile is added to m_lPassableTiles, remove it from any list of adjacent tiles received into your function. You're kind of doing something similar in your line with Contains... what if you annexed that if statement to include your recursive call? That should cut your recursive calls down from a million+ to... thousands at most, I imagine.

Thanks for the input everyone. I solved this by replacing the Recursive function with Dijkstra's Algorithm and it works perfectly.