I'm using a script that i found online that uses a kdTree to calculate the nearest point to an object on the surface of a mesh.
I have the following code in the OnDrawGizmos method that allows me to draw a circle that will orbit the surface of the object.
x = target.transform.position.x + ((Mathf.Cos(tValue)) * (radius));
z = target.transform.position.z + ((Mathf.Sin(tValue)) * (radius));
Gizmos.color = Color.yellow;
Gizmos.DrawWireSphere(new Vector3(x, y, z), 0.06f);
On the the object i am orbiting the "tValue" ranges from 0 to 6.3 to do a full orbit. My problem is that i am trying to calculate the tValue in the range 0-6.3 of an object that is near the central object. I have used my kdTree system to calculate the vector3 position on the surface of the object and it lines up perfectly.
I calculate the radius used in both the above and below equation with:
Vector3 RadiusDirection = (Vector3.ProjectOnPlane(orbitingSurfaceMeshPos, planet.transform.up) - Vector3.ProjectOnPlane(planet.transform.position, planet.transform.up));
float radius = RadiusDirection.magnitude;
However, when i try to calculate the t-value, i get a completely different value. I figured i could just "reverse" the "equation" and so i've been doing:
float temp = orbiting.z - planet.transform.position.z;
temp = temp / radius;
calculatedTvalue = (Mathf.Asin(temp));
What could i be doing wrong? I have tested my "reversing equation" in an empty scene and new script and it worked fine, if i just took the result of the orbit position calculation and directly reversed it. However, it doesn't work in my game.
Related
This is a question for Unity people or Math geniuses.
I'm making a game where I have a circle object that I can move, but I don't want it to intersect or go into other (static) circles in the world (Physics system isn't good enough in Unity to simply use that, btw).
It's in 3D world, but the circles only ever move on 2 axis.
I was able to get this working perfectly if circle hits only 1 other circle, but not 2 or more.
FYI: All circles are the same size.
Here's my working formula for 1 circle to move it to the edge of the colliding circle if intersecting:
newPosition = PositionOfStaticCircleThatWasJustIntersected + ((positionCircleWasMovedTo - PositionOfStaticCircleThatWasJustIntersected).normalized * circleSize);
But I can't figure out a formula if the moving circle hits 2 (or more) static circles at the same time.
One of the things that confuse me the most is the direction issue depending on how all the circles are positioned and what direction the moving circle is coming from.
Here's an example image of what I'm trying to do.
Since we're operating in a 2D space, let's approach this with some geometry. Taking a close look at your desired outcome, a particular shape become apparent:
There's a triangle here! And since all circles are the same radius, we know even more: this is an isosceles triangle, where two sides are the same length. With that information in hand, the problem basically boils down to:
We know what d is, since it's the distance between the two circles being collided with. And we know what a is, since it's the radius of all the circles. With that information, we can figure out where to place the moved circle. We need to move it d/2 between the two circles (since the point will be equidistant between them), and h away from them.
Calculating the height h is straightforward, since this is a right-angle triangle. According to the Pythagorean theorem:
// a^2 + b^2 = c^2, or rewritten as:
// a = root(c^2 - b^2)
float h = Mathf.Sqrt(Mathf.Pow(2 * a, 2) - Mathf.Pow(d / 2, 2))
Now need to turn these scalar quantities into vectors within our game space. For the vector between the two circles, that's easy:
Vector3 betweenVector = circle2Position - circle1Position
But what about the height vector along the h direction? Well, since all movement is on 2D space, find a direction that your circles don't move along and use it to get the cross product (the perpendicular vector) with the betweenVector using Vector3.Cross(). For
example, if the circles only move laterally:
Vector3 heightVector = Vector3.Cross(betweenVector, Vector3.up)
Bringing this all together, you might have a method like:
Vector3 GetNewPosition(Vector3 movingCirclePosition, Vector3 circle1Position,
Vector3 circle2Position, float radius)
{
float halfDistance = Vector3.Distance(circle1Position, circle2Position) / 2;
float height = Mathf.Sqrt(Mathf.Pow(2 * radius, 2) - Mathf.Pow(halfDistance, 2));
Vector3 betweenVector = circle2Position - circle1Position;
Vector3 heightVector = Vector3.Cross(betweenVector, Vector3.up);
// Two possible positions, on either side of betweenVector
Vector3 candidatePosition1 = circle1Position
+ betweenVector.normalized * halfDistance
+ heightVector.normalized * height;
Vector3 candidatePosition2 = circle1Position
+ betweenVector.normalized * halfDistance
- heightVector.normalized * height;
// Absent any other information, the closer position will be assumed as correct
float distToCandidate1 = Vector3.Distance(movingCirclePosition, candidatePosition1);
float distToCandidate2 = Vector3.Distance(movingCirclePosition, candidatePosition2);
if (distToCandidate1 < distToCandidate2){
return candidatePosition1;
}
else{
return candidatePosition2;
}
}
Hey there I am trying to rotate a line around its own center within the latlng system.
I got the angle and the two points. So I tried to append the rotation matrix, like this (following method takes the latitude and longitude of a point and the angle):
LatLng rotate(double lat, double long, double angle){
double rad = angle*pi/180;
double newLong = long*cos(rad)-lat*sin(rad);
double newLat = long* sin(rad) + lat*cos(rad);
return LatLng(newLat,newLong);
}
For example I got the point A (latitude:x,longitude:y) and the point B(latitude:x,longitude:y). Connecting these two points leads to a line. Now I want two rotate the line around it's own center with the above method, by calling:
LatLng newA = rotate(A.latitude,A.longitude);
LatLng newB = rotate(B.latitude,B.longitude);
But when I connect the two Points newA and NewB there is not the desired effect.
As #Abion47 clarified in his answer I need a rotation in 3-dimension, but how to do so? And is it possible with 2-dimension if it is a very small line?
So here's the rub. The problem I mentioned before is that a latitude-longitude pair are a pair of angles, not a 2D vector of a point on a graph, so trying to use them to rotate a point in 3D space on the surface of a sphere is going to run into its own problems. One thing that turns out, however, is that as long as you don't pick points that cross either the international date line or the poles, you can still use this trick by just pretending the angle pair is a 2D vector.
The real problem is that you are wanting to rotate the points around the midpoint, but your math is merely performing a straight rotation which will be rotating them around the origin instead (i.e. 0,0). You need to offset your "points" by the point you are using as a reference.
import 'dart:math';
LatLng rotate(LatLng coord, LatLng midpoint, double angle) {
// Make this constant so it doesn't have to be repeatedly recalculated
const piDiv180 = pi / 180;
// Convert the input angle to radians
final r = angle * piDiv180;
// Create local variables using appropriate nomenclature
final x = coord.longitude;
final y = coord.latitude;
final mx = midpoint.longitude;
final my = midpoint.latitude;
// Offset input point by the midpoint so the midpoint becomes the origin
final ox = x - mx;
final oy = y - my;
// Cache trig results because trig is expensive
final cosr = cos(r);
final sinr = sin(r);
// Perform rotation
final dx = ox * cosr - oy * sinr;
final dy = ox * sinr + oy * cosr;
// Undo the offset
return LatLng(dy + my, dx + mx);
}
Using this approach, I ended up with the following results:
The blue points are the input, the green point is the calculated midpoint, and the red points are each of the blue points passed through a 90 degree rotation.
(Note that the distance between the blue points appears to be farther than the distance between the red points. This is because I visualized the results in Google Maps which uses the Mercator projection, and that had the result of screwing with where the points appear to be relative to each other. If you were to visualize this on a globe, the points should appear the correct distance from each other.)
I am trying to have a gameobject in unity react with sound if another object is inside it. I want the gameobject to use the entering objects location to then see what voxel is closest and then play audio based on the voxel intensity/colour. Does anyone have any ideas? I am working with a dataset that is 512x256x512 voxels. I want it to work if the object is resized as well. Any help is much appreciated :).
The dataset I'm working with is a 3d .mhd medical scan of a body. Here is how the texture is added to the renderer on start:
for (int k = 0; k < NumberOfFrames; k++) {
string fname_ = "T" + k.ToString("D2");
Color[] colors = LoadData(Path.Combine (imageDir, fname_+".raw"));
_volumeBuffer.Add (new Texture3D (dim [0], dim [1], dim [2], TextureFormat.RGBAHalf, mipmap));
_volumeBuffer[k].SetPixels(colors);
_volumeBuffer [k].Apply ();
}
GetComponent<Renderer>().material.SetTexture("_Data", _volumeBuffer[0]);
The size of the object is defined by using the mdh header files spacing as well as voxel dimensions:
transform.localScale = new Vector3(mhdheader.spacing[0] * volScale, mhdheader.spacing[1] * volScale * dim[1] / dim[0], mhdheader.spacing[2] * volScale * dim[2] / dim[0]);
I have tried making my own function to get the index from the world by offsetting it to the beginning of the render mesh (not sure if this is right). Then, scaling it by the local scale. Then, multiplying by the amount of voxels in each dimension. However, I am not sure if my logic is right whatsoever... Here is the code I tried:
public Vector3Int GetIndexFromWorld(Vector3 worldPos)
{
Vector3 startOfTex = gameObject.GetComponent<Renderer>().bounds.min;
Vector3 localPos = transform.InverseTransformPoint(worldPos);
Vector3 localScale = gameObject.transform.localScale;
Vector3 OffsetPos = localPos - startOfTex;
Vector3 VoxelPosFloat = new Vector3(OffsetPos[0] / localScale[0], OffsetPos[1] / localScale[1], OffsetPos[2] / localScale[2]);
VoxelPosFloat = Vector3.Scale(VoxelPosFloat, new Vector3(voxelDims[0], voxelDims[1], voxelDims[2]));
Vector3Int voxelPos = Vector3Int.FloorToInt(VoxelPosFloat);
return voxelPos;
}
You can try setting up a large amount of box colliders and the OnTriggerEnter() function running on each. But a much better solution is to sort your array of voxels and then use simple math to clamp the moving objects position vector to ints and do some maths to map the vector to an index in the array. For example the vector (0,0,0) could map to voxels[0]. Then just fetch that voxels properties as you like. For a voxel application this would be a much needed faster calculation than colliders.
I figured it out I think. If anyone sees any flaw in my coding, please let me know :).
public Vector3Int GetIndexFromWorld(Vector3 worldPos)
{
Vector3 deltaBounds = rend.bounds.max - rend.bounds.min;
Vector3 OffsetPos = worldPos - rend.bounds.min;
Vector3 normPos = new Vector3(OffsetPos[0] / deltaBounds[0], OffsetPos[1] / deltaBounds[1], OffsetPos[2] / deltaBounds[2]);
Vector3 voxelPositions = new Vector3(normPos[0] * voxelDims[0], normPos[1] * voxelDims[1], normPos[2] * voxelDims[2]);
Vector3Int voxelPos = Vector3Int.FloorToInt(voxelPositions);
return voxelPos;
}
I am trying to simulate liquid conformity in a container. The container is a Unity cylinder and so is the liquid. I track current volume and max volume and use them to determine the coordinates of the center of where the surface should be. When the container is tilted, each vertex in the upper ring of the cylinder should maintain it's current local x and z values but have a new local y value that is the same height in the global space as the surface center.
In my closest attempt, the surface is flat relative to the world space but the liquid does not touch the walls of the container.
Vector3 v = verts[i];
Vector3 newV = new Vector3(v.x, globalSurfaceCenter.y, v.z);
verts[i] = transform.InverseTransformPoint(newV);
(I understand that inversing the point after using v.x and v.z changes them, but if I change them after the fact the surface is no longer flat...)
I have tried many different approaches and I always end up at this same point or a stranger one.
Also, I'm not looking for any fundamentally different approach to the problem. It's important that I alter the vertices of a cylinder.
EDIT
Thank you, everyone, for your feedback. It helped me make progress with this problem but I've reached another roadblock. I made my code more presentable and took some screenshots of some results as well as a graph model to help you visualize what's happening and give variable names to refer to.
In the following images, colored cubes are instantiated and given the coordinates of some of the different vectors I am using to get my results.
F(red) A(green) B(blue)
H(green) E(blue)
Graphed Model
NOTE: when I refer to capital A and B, I'm referring to the Vector3's in my code.
The cylinders in the images have the following rotations (left to right):
(0,0,45) (45,45,0) (45,0,20)
As you can see from image 1, F is correct when only one dimension of rotation is applied. When two or more are applied, the surface is flat, but not oriented correctly.
If I adjust the rotation of the cylinder after generating these results, I can get the orientation of the surface to make sense, but the number are not what you might expect.
For example: cylinder 3 (on the right side), adjusted to have a surface flat to the world space, would need a rotation of about (42.2, 0, 27.8).
Not sure if that's helpful but it is something that increases my confusion.
My code: (refer to graph model for variable names)
Vector3 v = verts[iter];
Vector3 D = globalSurfaceCenter;
Vector3 E = transform.TransformPoint(new Vector3(v.x, surfaceHeight, v.z));
Vector3 H = new Vector3(gsc.x, E.y, gsc.z);
float a = Vector3.Distance(H, D);
float b = Vector3.Distance(H, E);
float i = (a / b) * a;
Vector3 A = H - D;
Vector3 B = H - E;
Vector3 F = ((A + B)) + ((A + B) * i);
Instantiate(greenPrefab, transform).transform.position = H;
Instantiate(bluePrefab, transform).transform.position = E;
//Instantiate(redPrefab, transform).transform.position = transform.TransformPoint(F);
//Instantiate(greenPrefab, transform).transform.position = transform.TransformPoint(A);
//Instantiate(bluePrefab, transform).transform.position = transform.TransformPoint(B);
Some of the variables in my code and in the graphed model may not be necessary in the end, but my hope is it gives you more to work with.
Bear in mind that I am less than proficient in geometry and math in general. Please use Laymans's terms. Thank you!
And thanks again for taking the time to help me.
As a first step, we can calculate the normal of the upper cylinder surface in the cylinder's local coordinate system. Given the world transform of your cylinder transform, this is simply:
localNormal = inverse(transform) * (0, 1, 0, 0)
Using this normal and the cylinder height h, we can define the plane of the upper cylinder in normal form as
dot(localNormal, (x, y, z) - (0, h / 2, 0)) = 0
I am assuming that your cylinder is centered around the origin.
Using this, we can calculate the y-coordinate for any x/z pair as
y = h / 2 - (localNormal.x * x + localNormal.z * z) / localNormal.y
I am trying to calculate circular motion (orbit) around an object. The code i have gives me a nice circular orbit around the object. The problem is that when i rotate the object, the orbit behaves as though the object were not rotated.
I've put a really simple diagram below to try and explain it better. The left is what i get when the cylinder is upright, the middle is what i currently get when the object is rotated. The image on the right is what i would like to happen.
float Gx = target.transform.position.x - ((Mathf.Cos(currentTvalue)) * (radius));
float Gz = target.transform.position.z - ((Mathf.Sin(currentTvalue)) * (radius));
float Gy = target.transform.position.y;
Gizmos.color = Color.green;
Gizmos.DrawWireSphere(new Vector3(Gx, Gy, Gz), 0.03f);
How can i get the orbit to change with the objects rotation? I have tried multiplying the orbit poisition "new Vector3(Gx,Gy,Gz)" by the rotation of the object:
Gizmos.DrawWireSphere(target.transform.rotation*new Vector3(Gx, Gy, Gz), 0.03f);
but that didn't seem to do anything?
That is happening because you are calculating the vector (Gx, Gy, Gz) in world space coordinates, where the target object's rotations are not taken in consideration.
One way to solve your needs is to calculate this rotation using the target object's local space coordinates, and then convert them to world space coordinates. This will correctly make your calculations consider the rotation of the target object.
float Gx = target.transform.localPosition.x - ((Mathf.Cos(currentTvalue)) * (radius));
float Gz = target.transform.localPosition.z - ((Mathf.Sin(currentTvalue)) * (radius));
float Gy = target.transform.localPosition.y;
Vector3 worldSpacePoint = target.transform.TransformPoint(Gx, Gy, Gz);
Gizmos.color = Color.green;
Gizmos.DrawWireSphere(worldSpacePoint, 0.03f);
Notice that instead of target.transform.position, which retrieves the world space coordinates of the given transform, I am doing the calculations using the target.transform.localPosition, which retrieves the local space coordinates of the given transform.
Also, I am calling the TransformPoint() method, which converts the coordinates which I have calculated in local space to its corresponding values in world space.
Then you might safely call the Gizmos.DrawWireSphere() method, which requires world space coordinates to work correctly.