I'd like to draw the trajectory of an object that is moving circularly, but I do not know how to do it.
Could you tell me a good way?
I've not done a orbiting around something, but I am using Cos and Sin to generate static items around the object.
If you use TrailRenderer with the use of MathF cos and sin to rotate around an object.
var y = amplitude * MathF.cos(Time.timeSinceLevelLoaded * speed) + currentPosY
var x = amplitude * MathF.sin(Time.timeSinceLevelLoaded * speed) + currentPosX
I've not watched it, but "Board to bits" on youtube has a tutorial on the matter. of space orbiting for a planet playlist.
Hope this is the right direction for you.
Thank you for a lot of response.
I found it works with below...
void drawLine()
{
Vector3[] points = new Vector3[segments+1];
for (int i = 0; i< segments; i++)
{
float angle = ((float)i / (float)segments) * 360 * Mathf.Deg2Rad;
float x = Mathf.Sin(angle) * radius;
float z = Mathf.Cos(angle) * radius;
points[i] = new Vector3(x, 0f, z);
}
points[segments] = points[0];
lr.positionCount = segments + 1;
lr.SetPositions(points);
}
Related
So I was trying to follow the code in this question to get a turret that can fire ballistic projectiles with a fixed starting velocity and no drag to a given point on a 3D surface.
Find an angle to launch the projectile at to reach a specific point
But It's not quite working. The turret ends up aiming too high when the target is close, and too low when the target is further away. There is of course a specific distance at which it does hit the target but that distance is arbitrary, so that's not at all helpful to me.
The way the error scales makes me think I have a multiplication mistake, or am missing some multiplication or division, but I can't for the life of me figure out where I am going wrong. Can anyone point me in the right direction?
Code Below:
float CalculateAngle(float velocity)
{
float gravity = -Physics.gravity.y;
Vector3 modPos = target.position;
if (modPos.x < 0) modPos.x -= 2 * modPos.x;
if (modPos.y < 0) modPos.y -= 2 * modPos.y;
if (modPos.z < 0) modPos.z -= 2 * modPos.z;
modPos.x /= 10;
modPos.y /= 10;
modPos.z /= 10;
float deltaX = modPos.x - FirePoint.position.x;
float deltaZ = modPos.z - FirePoint.position.z;
float deltaY = modPos.y - FirePoint.position.y;
float horzDelta = Mathf.Sqrt(deltaX * deltaX + deltaZ * deltaZ);
float RHSFirstPart = (velocity * velocity) / (gravity * horzDelta);
float RHSSecondPart = Mathf.Sqrt(((velocity * velocity) * ((velocity * velocity) - (2 * gravity * deltaY))/ (gravity * gravity * horzDelta * horzDelta)) - 1);
float tanθ = RHSFirstPart - RHSSecondPart;
float angle = Mathf.Atan2(tanθ, 1) * Mathf.Rad2Deg;
if (angle < 0) return angle;
return -angle;
}
Edit 1:
Still struggling heavily with this. I just can't get the math to work. I went back to the original root of the knowledge here https://physics.stackexchange.com/questions/56265/how-to-get-the-angle-needed-for-a-projectile-to-pass-through-a-given-point-for-t then wrote a function that did the exact equation given in the answers, copying the input values and everything. Except when I run it it fails, as one of the values that needs to be squared is negative which throws a NaN. I assume I am going wrong somewhere in my equation but I've gone over it a hundred times and I am not spotting the error. My code:
float CalculateAngle3(float velocity)
{
float deltaX = 500;
float deltaY = 20;
float v = 100;
float vSqr = v * v;
float g = 9.81f * 9.81f;
float a = vSqr * (vSqr - 2 * g * deltaY);
float b = (g * g) * (deltaX * deltaX);
float c = a / b - 1;
float d = Mathf.Sqrt(c); //c is negitive causing an NaN
float e = vSqr / g * deltaX;
float tanθ = e - d;
return tanθ;
}
Edit 2:
Gave up. This guy solved it so I am just going to use his logic instead
: P
https://www.forrestthewoods.com/blog/solving_ballistic_trajectories/
Using it like such:
Vector3 s0;
Vector3 s1;
if (fts.solve_ballistic_arc(FirePoint.position, bomb.StartingVelocity.z, target.position, -Physics.gravity.y, out s0, out s1) > 0)
{
targetPosition = transform.position + s1;
SafetyEnabled = false;
}
else
{
//Don't fire if we don't have a solution
SafetyEnabled = true;
}
I'm going to leave the question open for now since it's still technically not answered. I still don't know why the original implementation wasn't working.
It is possible your quadratic formula is incorrect (I do not know why you did not code a separate small function that solves the quadratic equation for any three given coefficients, to make your code more readable and less prone to errors)
float RHSFirstPart = velocity / (gravity * horzDelta);
float RHSSecondPart = Mathf.Sqrt(RHSFirstPart*RHSFirstPart - 2*RHSFirstPart*deltaY/horzDelta - 1);
float tanθ = RHSFirstPart - RHSSecondPart;
A comment: In most applications we do not really need the actual angle but the values of cos(angle) and sin(angle) because these are the components of the unit vector which usually is sought (just like in your case). So no need to use inverse trigonometry to find an actual number, which slows down calculations and is may introduce unnecessary round-off errors.
I need to shoot a ball from any height and make it bounce on a target position defined by the user. The angle of launch is also given. I've tried a couple of solutions so far:
Vector3 calcBallisticVelocityVector(Vector3 source, Vector3 target, float angle) {
Vector3 direction = target - source;
float h = direction.y;
direction.y = 0;
float distance = direction.magnitude;
float a = angle * Mathf.Deg2Rad;
direction.y = distance * Mathf.Tan(a);
distance += h/Mathf.Tan(a);
// calculate velocity
float velocity = Mathf.Sqrt(distance * Physics.gravity.magnitude / Mathf.Sin(2*a));
return velocity * direction.normalized;
}
Vector3 calcBallisticVelocityVector2(Vector3 source, Vector3 target, float angle) {
float distance = (target.Planar() - source.Planar()).magnitude;
float a = target.y - source.y - distance;
float halfGravity = -Physics.gravity.magnitude * 0.5f;
float distanceSquared = distance * distance;
float theta = Mathf.Deg2Rad * angle;
float cosSquared = Mathf.Cos(theta) * Mathf.Cos(theta);
float b = distanceSquared / cosSquared;
float speed = Mathf.Sqrt((halfGravity * b) / a);
Vector3 velocity = (target.Planar() - source.Planar()).normalized * Mathf.Cos(theta);
velocity.y = Mathf.Sin(theta);
return velocity * speed;
}
The results I'm getting is that even the ball does go into the direction is expected, it falls earlier than it should be so the speed calculated by these methods seems to be lower than what is actually required to hit the target position.
Rigidbody's mass is set to 1, Gravity is (0, -98, 0), rigid body's drag and angular drag is set to 0. What other variables could be affecting this behavior?
EDIT: One thing I forgot to mention is that I'm setting the resulting vector as rigid body's velocity, so I'm not using via the apply force method.
I adapted code gotten from here: https://answers.unity.com/questions/1131176/projectile-motion.html and now I'm getting the results I was expecting. I can always hit the target position at whatever angle I input.
private Vector3 calcBallisticVelocityVector(Vector3 initialPos, Vector3 finalPos, float angle)
{
var toPos = initialPos - finalPos;
var h = toPos.y;
toPos.y = 0;
var r = toPos.magnitude;
var g = -Physics.gravity.y;
var a = Mathf.Deg2Rad * angle;
var vI = Mathf.Sqrt (((Mathf.Pow (r, 2f) * g)) / (r * Mathf.Sin (2f * a) + 2f * h * Mathf.Pow (Mathf.Cos (a), 2f)));
Vector3 velocity = (finalPos.Planar() - initialPos.Planar()).normalized * Mathf.Cos(a);
velocity.y = Mathf.Sin(a);
return velocity * vI;
}
I want to proceduraly generate meshes. I created a method to supply the vertices of a circle. The idea is that it creates a shape in 2d and then rotates it in 3d assuming that "rotation" is the vector of the shapes normal axis.
public List<Vector3> Loop (Vector3 center, Vector3 rotation, float radius, int divisions)
{
List<Vector3> loop = new List<Vector3>();
for(int p = 0; p < divisions; p++)
{
float u = (float)Math.Cos(2 * Math.PI * p / divisions) * radius;
float v = (float)Math.Sin(2 * Math.PI * p / divisions) * radius;
float x = 0;
float y = 0;
float z = 0;
// Apply rotation to u & v to get x, y, z
loop.Add(new Vector3(x, y, z));
}
return loop;
}
Creating the circle in 2d (u & v) was super easy but when I looked into applying 3d rotations, it seemed to be a complete rabbit hole completely beyond my comprehension.
Is there a way to use existing API to do this?
I would pass in an axis parameter that you are rotating rotation around, then use Cross products to find the "up" direction for the "forward" that is the normal of the circle.
Use Quaternion.LookRotation, then Quaternion * Vector3 to apply the rotation to the position:
public List<Vector3> Loop (Vector3 center, Vector3 rotation, Vector3 axis, float radius, int divisions)
{
List<Vector3> loop = new List<Vector3>();
for(int p = 0; p < divisions; p++)
{
float u = (float)Math.Cos(2 * Math.PI * p / divisions) * radius;
float v = (float)Math.Sin(2 * Math.PI * p / divisions) * radius;
Vector3 fromPosition = new Vector3(u, v, 0f);
Vector3 up = Vector3.Cross(rotation.normalized, axis.normalized);
Quaternion rot = Quaternion.LookRotation(rotation, up);
loop.Add(rot * fromPosition);
}
return loop;
}
So you could do something like: List<Vector3> res = Loop(Vector3.zero, Vector3.up, Vector3.right, 10f, 20);
I am working on adding a helicopter to my 2d game and I need it to move in circular motion whilst moving on the x axis as well. Below you can find the code that I am using which uses the mathematical circle equation.
angle += speed * Time.deltaTime; //if you want to switch direction, use -= instead of +=
float x = startPoint.x + Mathf.Cos(angle) * radius;
float y = startPoint.y + Mathf.Sin(angle) * radius;
transform.position = new Vector2(x + 2, y);
The helicopter is rotating correctly but I can't figure out how I can make it move along the x axis. Concept image of how it should work below:
1) Make an empty game object
2) Parent your box to the empty game object
3) rotate the box around the empty game object
4) move the empty game object to the side
If you want to avoid adding an empty parent, you can keep track of the center of rotation separately, rotate around it, and move it over time.
public class hello_rotate : MonoBehaviour
{
float angle = 0;
float radius = 1;
float speed = 10;
float linear_speed = 1;
Vector2 centerOfRotation;
// Start is called before the first frame update
void Start()
{
centerOfRotation = transform.position;
}
// Update is called once per frame
void Update()
{
centerOfRotation.x = centerOfRotation.x + linear_speed * Time.deltaTime;
angle += speed * Time.deltaTime; //if you want to switch direction, use -= instead of +=
float x = centerOfRotation.x + Mathf.Cos(angle) * radius;
float y = centerOfRotation.y + Mathf.Sin(angle) * radius;
transform.position = new Vector2(x + 2, y);
}
}
i'm trying to get the tangent vector for each point on the circle , i tried to use the derivative for the circle equation, but the result looks off in the viewport, so i'm wondering if i can find some help here
the code
public void OnDrawGizmos(){
step = (360.0f * Mathf.Deg2Rad) / numberOfPoints ;
CreateVertices();
}
void CreateVertices()
{
Points.Clear();
Normals.Clear();
Tangents.Clear();
float dynamicAngle = 0.0f;
for (int i = 0; i <= numberOfPoints; i++)
{
Vector3 point;
point.x = transform.position.x + Radius * Mathf.Cos(dynamicAngle);
point.y = transform.position.y + Radius * Mathf.Sin(dynamicAngle);
point.z = transform.position.z;
dynamicAngle = dynamicAngle + step;
if (i >= 1)
{
Gizmos.color = Color.red;
Gizmos.DrawLine(Points[i - 1], point);
Gizmos.color = Color.white;
}
Points.Add(point);
CalculateNormals(dynamicAngle ,point);
CalculateTangents(dynamicAngle,i , point);
}
}
void CalculateNormals(float dynamicAngle , Vector3 point)
{
Vector3 Normal = (point - transform.position).normalized;
Gizmos.color = Color.magenta;
Gizmos.DrawLine(Normal, point);
Gizmos.color = Color.white;
Normals.Add(Normal);
}
void CalculateTangents(float dynamicAngle,int i ,Vector3 point)
{
Vector3 tangent;
tangent = new Vector3(-Normals[i].y, Normals[i].x, 0);
tangent.Normalize();
Gizmos.color = Color.blue;
Gizmos.DrawLine( point, tangent);
Gizmos.color = Color.white;
Tangents.Add(tangent);
}
Blue is the tangents purple is the normals, as you can see they are not perpendicular:
To understand my issue better here is a gif from unity viewport:
Since you already calculated the normals you can use the cross product to get the corresponding tangents
Vector3 up = new Vector3(0, 0, 1); // up side of your circle
Vector3 tangent = Vector3.Cross(normal, up);
If you only need to use circles on a specific plane you can also use this simplification
Vector3 tangent = new Vector3(-normal.y, normal.x, 0);
Edit:
The normals and tangents are direction vectors. They point from point in the direction the normal / tangent whould point. To draw the tangent, you have to pass the correct start and end points of the line by using
Gizmos.DrawLine(point, point + tangent);
If you move the GameObject away from the origin you will notice that the normals also get deformed, this has the same reason.
You are using 2D parametric equations:
x = x0 + r*cos(a)
y = y0 + r*sin(a)
z = z0
a = <0,2*Pi>
Tangent is unit circle coordinate with center (0,0,0) but shifted by 90 degrees:
tx = cos(a (+/-) pi/4)
ty = sin(a (+/-) pi/4)
tz = 0
Similarly bi-tangent is:
bx = (+/-) cos(a)
by = (+/-) sin(a)
bz = 0
and finally normal is
nx = 0
ny = 0
nz = (+/-) 1
The signs depends on your coordinate system conventions and movement direction.