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How can i find the middle of a Hexgrid?

So ive created a code which will use my Standard hexagon Node from Godot and istance it for a given size into a hexgrid, now i wanted to find the exact middle of this Hexgrid to position my player there eg. move the Nodes along the X and Z axis to the standard position of the map 0,0,0.
I thought the exact middle of the Hexgrid is Axis X - Size of the X Axis / 2, Axis Z - Size of the Y Axis / 2.
But this just doesnt seem to work. Any suggestions on how to finde the middle of the Hexgrid and how to move it along the axis?
The Code for the middle looks like this:
public void GenerateGrid()
{
for (int y = 0; y < gridSize.Y; y++)
{
for (int x = 0; x < gridSize.X; x++)
{
Vector3 newPos = GetPositionFromCurrentHex(new Vector2(x, y));
Node3D generator_scene = (Node3D) ResourceLoader.Load<PackedScene>(tilePath).Instantiate();
generator_scene.Position = new Vector3(newPos.X - (gridSize.X / 2.0f), newPos.Y, newPos.Z - (gridSize.Y/ 2.0f));
if (isFlatTopped)
{
generator_scene.RotateY(Mathf.DegToRad(90));
}
AddChild(generator_scene);
}
}
}
And for the Calculation of the Hexgrid:
public Vector3 GetPositionFromCurrentHex(Vector2 coordinate)
{
float col = coordinate.X;
float row = coordinate.Y;
float width;
float height;
float xPos;
float yPos;
bool shouldOffset;
float horizontalDistance;
float verticalDistance;
float offset;
float size = outerSize;
if (!isFlatTopped)
{
shouldOffset = (row % 2) == 0;
width = Mathf.Sqrt(3) * size;
height = 2f * size;
horizontalDistance = width;
verticalDistance = height * (3f / 4f);
offset = (shouldOffset) ? width / 2 : 0;
xPos = (col * (horizontalDistance)) + offset;
yPos = (row * verticalDistance);
}
else
{
shouldOffset = (col % 2) == 0;
width = 2f * size;
height = Mathf.Sqrt(3f) * size;
horizontalDistance = width * (3f / 4f);
verticalDistance = height;
offset = (shouldOffset) ? height / 2 : 0;
xPos = (col * (horizontalDistance));
yPos = (row * verticalDistance) - offset;
}
return new Vector3(xPos, 0, yPos);
}

Answer depends on how you define center in different cases, for example
Is your hexgrid flat top or pointy top?
Is the topmost row of your hexgrid also leftmost or not (offset of rows)
Do you expect your "center" of the hexgrid to be also center of an hexagon, or it can be a point along edge of some hexagons.
If the number of rows and columns are odd, you can get away with calculating the coordinates of 4 corner points (topleft, topright, botleft, botright) and average them. If your grid is pointy-top this is also center of the middle hexagon, if your grid is flat-top it is on the edge between two hexagons.

Raycast not capturing all Vector coordinates

I have a gameobject that occupies the whole screen just for testing purposes. I'm drawing a line btw. What I'm trying to achieve is if the mouse position hits a gameobject it will store the vector2 coordinates in a list. But raycast is not storing all the coordinates. Below is my code
private void Update()
{
if (Input.GetMouseButton(0))
{
Vector2 mousePos = Input.mousePosition;
Vector2 Pos = _camera.ScreenToWorldPoint(mousePos);
if(!mousePositions.Contains(Pos))
mousePositions.Add(Pos);
if (Physics.Raycast(Camera.main.ScreenPointToRay(mousePos), out RaycastHit hit))
{
Vector2 textureCoord = hit.textureCoord;
int pixelX = (int)(textureCoord.x * _templateDirtMask.width);
int pixelY = (int)(textureCoord.y * _templateDirtMask.height);
Vector2Int paintPixelPosition = new Vector2Int(pixelX, pixelY);
if (!linePositions.Contains(paintPixelPosition))
linePositions.Add(paintPixelPosition);
foreach (Vector2Int pos in linePositions)
{
int pixelXOffset = pos.x - (_brush.width / 2);
int pixelYOffset = pos.y - (_brush.height / 2);
for (int x = 0; x < _brush.width; x++)
{
for (int y = 0; y < _brush.height; y++)
{
_templateDirtMask.SetPixel(
pixelXOffset + x,
pixelYOffset + y,
Color.black
);
}
}
}
_templateDirtMask.Apply();
}
}
}
Everytime I checked the element count mousePositions are always greater than linePositions. I don't know what's causing this

the element count mousePositions are always greater than linePosition
well it is quite simple: In
int pixelX = (int)(textureCoord.x * _templateDirtMask.width);
int pixelY = (int)(textureCoord.y * _templateDirtMask.height);
you are casting to int and cut off any decimals after the comma (basically like doing Mathf.FloorToInt).
So you can totally have multiple mouse positions which result in float pixel positions like e.g.
1.2, 1.2
1.4, 1.7
1.02, 1.93
...
all these will map to
Vector2Int paintPixelPosition = new Vector2Int(1, 1);
Besides, you might want to look at some better line drawing algorithms like e.g. this simple one
And then note that calling SetPixel repeatedly is quite expensive. You want to do a single SetPixels call like e.g.
var pixels = _templateDirtMask.GetPixels();
foreach (Vector2Int pos in linePositions)
{
int pixelXOffset = pos.x - (_brush.width / 2);
int pixelYOffset = pos.y - (_brush.height / 2);
for (int x = 0; x < _brush.width; x++)
{
for (int y = 0; y < _brush.height; y++)
{
pixels[(pixelXOffset + x) + (pixelYOffset + y) * _templateDirtMask.width] = Color.black;
}
}
}
_templateDirtMask.SetPixels(pixels);
_templateDirtMask.Apply();

It happens because there is really could be a case, when several elements from mousePositions are associated with one elment from linePositions.
Rough example: your texture resolution is only 1x1px. In this case you linePositons will contain only one element. And this element will be associated with all elements from mosePositions.
So, relation of the number of elements in these lists depends on relation of your texture and screen resolutions.

Getting weird results from terrain generation sys using 2D Perlin Noise

I am trying to make a terrain generation system in Unity, similar to Minecraft's, but using Unity's Perlin Noise function (so only 2D noise).
So I have a 16x16x16 chunk with a vector2int that has it's position (so like, if x & z = 0, then the blocks inside are from 0 to 16 in world coordinates).
This is how I'm trying to generate the height map of a chunk:
public void generate(float scale) {
GameObject root = new GameObject("Root");
// this.z & this.x are the chunk coordinates, size is 16
for(int z = this.z * size; z < (this.z + size); ++z) {
for (int x = this.x * size; x < (this.x + size); ++x) {
float[] coord = new float[2] { (float)x / size * scale,
(float)z / size * scale };
Debug.LogFormat("<color='blue'>Perlin coords |</color> x: {0}; y: {1}", coord[0], coord[1]);
float value = Mathf.PerlinNoise(coord[0], coord[1]);
// temporary
GameObject Cube = GameObject.CreatePrimitive(PrimitiveType.Cube);
Cube.transform.position = new Vector3(x, value, z);
Cube.transform.parent = root.transform;
}
}
return;
}
The results are... bad. See for yourself:
What can I do?

It looks good, looks just scrunched on the y transform.
float value = Mathf.PerlinNoise(coord[0], coord[1]);
This is going to give you problems, I'm not sure what coord[0] and coord[1] are but Mathf.PerlinNoise will return a random float between coord[0] and coord[1], so a random float will never be able to produce well aligned tiles.
Better off doing something like
int numTilesHigh = Random.Range(0,15);
for (int i = 0; i < numTilesHigh; i++) {
GameObject Cube = GameObject.CreatePrimitive(PrimitiveType.Cube);
Cube.transform.position = new Vector3(x, <cube height> * i, z);
Cube.transform.parent = root.transform;
}
ps I kind of like your screen shot, not in a minecraft way but it does look cool : - )

How can i create a plane out of many meshes?

What i want to do is to extrude a mesh plane.
The plane is in red in the scene view. Each mesh have two triangles.
First i don't understand what is the Res X and Res Z are for.
What i want to create first is a plane from vertices and triangles in size of 16x16 or any other size by height(Length should be height) and width.
But after i set all the properties to 16 the plane is built from 15x15 meshes not 16x16.
And my main goal is now to extrude the plane. I mean to use OnMouseDown and by a click on the plane to find the closet and neighbours of the vertices from where i clicked on and to extrude this vertice/s. Extrude i mean for example only the z to change the vertices i clicked on position on z only.
Something the same idea like in this image. Marked it in red circle:
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class meshPlane : MonoBehaviour
{
public int length;
public int width;
public int resX;
public int resZ;
private MeshFilter meshf;
private Mesh mesh;
private Vector3[] vertices;
private void Start()
{
GenerateOrigin();
}
private void GenerateOrigin()
{
// You can change that line to provide another MeshFilter
meshf = GetComponent<MeshFilter>();
mesh = new Mesh();
meshf.mesh = mesh;
mesh.Clear();
#region Vertices
vertices = new Vector3[resX * resZ];
for (int z = 0; z < resZ; z++)
{
// [ -length / 2, length / 2 ]
float zPos = ((float)z / (resZ - 1) - .5f) * length;
for (int x = 0; x < resX; x++)
{
// [ -width / 2, width / 2 ]
float xPos = ((float)x / (resX - 1) - .5f) * width;
vertices[x + z * resX] = new Vector3(xPos, 0f, zPos);
}
}
#endregion
#region Normales
Vector3[] normales = new Vector3[vertices.Length];
for (int n = 0; n < normales.Length; n++)
normales[n] = Vector3.up;
#endregion
#region UVs
Vector2[] uvs = new Vector2[vertices.Length];
for (int v = 0; v < resZ; v++)
{
for (int u = 0; u < resX; u++)
{
uvs[u + v * resX] = new Vector2((float)u / (resX - 1), (float)v / (resZ - 1));
}
}
#endregion
#region Triangles
int nbFaces = (resX - 1) * (resZ - 1);
int[] triangles = new int[nbFaces * 6];
int t = 0;
for (int face = 0; face < nbFaces; face++)
{
// Retrieve lower left corner from face ind
int i = face % (resX - 1) + (face / (resZ - 1) * resX);
triangles[t++] = i + resX;
triangles[t++] = i + 1;
triangles[t++] = i;
triangles[t++] = i + resX;
triangles[t++] = i + resX + 1;
triangles[t++] = i + 1;
}
#endregion
mesh.vertices = vertices;
mesh.normals = normales;
mesh.uv = uvs;
mesh.triangles = triangles;
mesh.RecalculateBounds();
}
}

When you say "the plane is built from 15x15 meshes" you mean the plane is built from 15x15 squares. That whole plane is the mesh.
ResX and ResZ are how many points there are in each direction. You get one less square because you need two edges for the first square. You need another two for each square you add, but they can share an edge with the previous one so you need only one more.
To make your mesh clickable you need to add a mesh collider to your gameobject and assign the mesh you generate to it. Then, you can use the camera class to get a ray, put that in a raycast and if your raycast hits anything you can use the triangle index and the triangles array you created to get the three points of the triangle that was hit. In addition you can see which weight in the barycentric coordinates is bigger to know which exact vertex your click was closest to. And finally, now that you have the exact vertex you can modify its height.

GDI+ curve "overflowing"

I'm currently using GDI+ to draw a line graph, and using Graphics.DrawCurve to smooth out the line. The problem is that the curve doesn't always match the points I feed it, and that makes the curve grow out of the graph frame in some points, as seen below(red is Graphics.DrawLines, green is Graphics.DrawCurve).
How would I go about solving this?

The simplest solution is to set a tension:
The green curve is drawn with the default tension, the blue one set a tension of 0.1f:
private void panel1_Paint(object sender, PaintEventArgs e)
{
e.Graphics.SmoothingMode = SmoothingMode.AntiAlias;
e.Graphics.DrawLines(Pens.Red, points.ToArray());
e.Graphics.DrawCurve(Pens.Green, points.ToArray());
e.Graphics.DrawCurve(Pens.Blue, points.ToArray(), 0.1f);
}
You will need to test what is the best compromise, 0.2f is still ok, 0.3f is already overdrawing quite a bit..
For a really good solution you will need to use DrawBeziers. This will let you draw curves that can go through the points without any overdrawing and with full control of the radius of the curves; but to to so you will need to 'find', i.e. calculate good control points, which is anything but trivial..:
This result is by no means perfect but already complicated enough.. I have displayed the curve points and their respective control points in the same color. For each point there is an incoming and an outgoing control point. For a smooth curve they need to have the same tangents/gradients in their curve points.
I use a few helper functions to calculate a few things about the segments:
A list of gradients
A list of signs of the gradients
A list of segment lengths
Lists of horizontal and of vertical gaps between points
The main function calculates the array of bezier points, that is the curve points and between each pair the previous left and the next right control points.
In the Paint event it is used like this:
List<PointF> bezz = getBezz(points);
using (Pen pen = new Pen(Color.Black, 2f))
e.Graphics.DrawBeziers(pen, bezz.ToArray());
Here are the functions I used:
List<float> getGradients(List<PointF> p)
{
List<float> grads = new List<float>();
for (int i = 0; i < p.Count - 1; i++)
{
float dx = p[i + 1].X - p[i].X;
float dy = p[i + 1].Y - p[i].Y;
if (dx == 0) grads.Add(dy == 0 ? 0 : dy > 0 ?
float.PositiveInfinity : float.NegativeInfinity);
else grads.Add(dy / dx);
}
return grads;
}
List<float> getLengths(List<PointF> p)
{
List<float> lengs = new List<float>();
for (int i = 0; i < p.Count - 1; i++)
{
float dx = p[i + 1].X - p[i].X;
float dy = p[i + 1].Y - p[i].Y;
lengs.Add((float)Math.Sqrt(dy * dy + dx * dx));
}
return lengs;
}
List<float> getGaps(List<PointF> p, bool horizontal)
{
List<float> gaps = new List<float>();
for (int i = 0; i < p.Count - 1; i++)
{
float dx = p[i + 1].X - p[i].X;
float dy = p[i + 1].Y - p[i].Y;
gaps.Add(horizontal ? dx : dy);
}
return gaps;
}
List<int> getSigns(List<float> g)
{
return g.Select(x => x > 0 ? 1 : x == 0 ? 0 : -1).ToList();
}
And finally the main function; here I make a distinction: Extreme points ( minima & maxima) should have their control points on the same height as the points themselves. This will prevent vertical overflowing. They are easy to find: The signs of their gradients will always altenate.
Other points need to have the same gradient for incoming and outcoming control points. I use the average between the segments' gradients. (Maybe a weighed average would be better..) And I weigh their distance according to the segment lengths..
List<PointF> getBezz(List<PointF> points)
{
List<PointF> bezz = new List<PointF>();
int pMax = points.Count;
List<float> hGaps = getGaps(points, true);
List<float> vGaps = getGaps(points, false);
List<float> grads = getGradients(points);
List<float> lengs = getLengths(points);
List<int> signs = getSigns(grads);
PointF[] bezzA = new PointF[pMax * 3 - 2];
// curve points
for (int i = 0; i < pMax; i++) bezzA[i * 3] = points[i];
// left control points
for (int i = 1; i < pMax; i++)
{
float x = points[i].X - hGaps[i - 1] / 2f;
float y = points[i].Y;
if (i < pMax - 1 && signs[i - 1] == signs[i])
{
float m = (grads[i-1] + grads[i]) / 2f;
y = points[i].Y - hGaps[i-1] / 2f * m * vGaps[i-1] / lengs[i-1];
}
bezzA[i * 3 - 1] = new PointF(x, y);
}
// right control points
for (int i = 0; i < pMax - 1; i++)
{
float x = points[i].X + hGaps[i] / 2f;
float y = points[i].Y;
if (i > 0 && signs[i-1] == signs[i])
{
float m = (grads[i-1] + grads[i]) / 2f;
y = points[i].Y + hGaps[i] / 2f * m * vGaps[i] / lengs[i];
}
bezzA[i * 3 + 1] = new PointF(x, y);
}
return bezzA.ToList();
}
Note that I didn't code for the case of points with the same x-coordinate. So this is ok for 'functional graphs' but not for, say figures, like e.g. stars..

Maybe you just want to look at the "overshooting the bounds" problem as not a problem with the overshoot, but with the bounds. In which case, you can determine the actual bounds of a curve using the System.Drawing.Drawing2D.GraphicsPath object:
GraphicsPath gp = new GraphicsPath();
gp.AddCurve(listOfPoints);
RectangleF bounds = gp.GetBounds();
You can draw that GraphicsPath directly:
graphics.DrawPath(Pens.Black, gp);
As far as solving the bounds problem, the line necessarily overshoots the vertex on some axis. It's easier to see this fact when the lines are aligned to the bounds.
Given these points:
In order for them to be curved, they must exceed their bounds in some way:
If you never want to exceed their vertical bounds, you could simply ensure that the bezier handles have the same Y value as the vertex, but they will overshoot on the X:
Or vice-versa:
You could deliberately undershoot just enough to avoid the way curves can overshoot. This can be done by swapping the bezier handles, which would maybe be at the line-centers, with the vertices: