Related
I'm attempting to convert from state vectors (position and speed) into Kepler elements, however I'm running into problems where a negative velocity or position will give me wrong results when trying to calculate true anomaly.
Here are the different ways I'm trying to calculate the True Anomaly:
/// <summary>
/// https://en.wikipedia.org/wiki/True_anomaly#From_state_vectors
/// </summary>
public static double TrueAnomaly(Vector4 eccentVector, Vector4 position, Vector4 velocity)
{
var dotEccPos = Vector4.Dot(eccentVector, position);
var talen = eccentVector.Length() * position.Length();
talen = dotEccPos / talen;
talen = GMath.Clamp(talen, -1, 1);
var trueAnomoly = Math.Acos(talen);
if (Vector4.Dot(position, velocity) < 0)
trueAnomoly = Math.PI * 2 - trueAnomoly;
return trueAnomoly;
}
//sgp = standard gravitational parameter
public static double TrueAnomaly(double sgp, Vector4 position, Vector4 velocity)
{
var H = Vector4.Cross(position, velocity).Length();
var R = position.Length();
var q = Vector4.Dot(position, velocity); // dot product of r*v
var TAx = H * H / (R * sgp) - 1;
var TAy = H * q / (R * sgp);
var TA = Math.Atan2(TAy, TAx);
return TA;
}
public static double TrueAnomalyFromEccentricAnomaly(double eccentricity, double eccentricAnomaly)
{
var x = Math.Sqrt(1 - Math.Pow(eccentricity, 2)) * Math.Sin(eccentricAnomaly);
var y = Math.Cos(eccentricAnomaly) - eccentricity;
return Math.Atan2(x, y);
}
public static double TrueAnomalyFromEccentricAnomaly2(double eccentricity, double eccentricAnomaly)
{
var x = Math.Cos(eccentricAnomaly) - eccentricity;
var y = 1 - eccentricity * Math.Cos(eccentricAnomaly);
return Math.Acos(x / y);
}
Edit: another way of doing it which Spectre pointed out:
public static double TrueAnomaly(Vector4 position, double loP)
{
return Math.Atan2(position.Y, position.X) - loP;
}
Positions are all relative to the parent body.
These functions all agree if position.x, position.y and velocity.y are all positive.
How do I fix these so that I get a consistent results when position and velocity are negitive?
Just to clarify: My angles appear to be sort of correct, just pointing in the wrong quadrant depending on the position and or velocity vectors.
Yeah so I was wrong, the above all do return the correct values after all.
So I found an edge case where most of the above calculations fail.
Given position and velocity:
pos = new Vector4() { X = -0.208994076275941, Y = 0.955838328099748 };
vel = new Vector4() { X = -2.1678187689294E-07, Y = -7.93096769486992E-08 };
I get some odd results, ie ~ -31.1 degrees, when I think it should return ` 31.1 (non negative). one of them returns ~ 328.8.
However testing with this position and velocity the results apear to be ok:
pos = new Vector4() { X = -0.25, Y = 0.25 };
vel = new Vector4() { X = Distance.KmToAU(-25), Y = Distance.KmToAU(-25) };
See my answer for extra code on how I'm testing and the math I'm using for some of the other variables.
I'm going around in circles on this one. this is a result of a bug in my existing code that shows up under some conditions but not others.
I guess the real question now is WHY am I getting different results with position/velocity above that don't match to my expectations or each other?
Assuming 2D case... I am doing this differently:
compute radius of semi axises and rotation
so you need to remember whole orbit and find 2 most distant points on it that is major axis a. The minor axis b usually is 90 deg from major axis but to be sure just fins 2 perpendicularly most distant points on your orbit to major axis. So now you got both semi axises. The initial rotation is computed from the major axis by atan2.
compute true anomaly E
so if center is x0,y0 (intersection of a,b or center point of both) initial rotation is ang0 (angle of a) and your point on orbit is x,y then:
E = atan2(y-y0,x-x0) - ang0
However in order to match Newton/D'Alembert physics to Kepler orbital parameters you need to boost the integration precision like I did here:
Is it possible to make realistic n-body solar system simulation in matter of size and mass?
see the [Edit3] Improving Newton D'ALembert integration precision even more in there.
For more info and equations see:
Solving Kepler's equation
[Edit1] so you want to compute V I see it like this:
As you got your coordinates relative to parent you can assume they are already in focal point centered so no need for x0,y0 anymore. Of coarse if you want high precision and have more than 2 bodies (focal mass + object + proximity object(s) like moons) then the parent mass will no longer be in focal point of orbit but close to it ... and to remedy you need to use real focal point position so x0,y0 again... So how to do it:
compute center point (cx,cy) and a,b semi axises
so its the same as in previous text.
compute focal point (x0,y0) in orbit axis aligned coordinates
simple:
x0 = cx + sqrt( a^2 + b^2 );
y0 = cy;
initial angle ang0 of a
let xa,ya be the intersection of orbit and major axis a on the side with bigger speeds (near parent object focus). Then:
ang0 = atan2( ya-cy , xa-cx );
and finally the V fore any of yours x,y
V = atan2( y-y0 , x-x0 ) - ang0;
Ok so on further testing it appears my original calcs do all return the correct values, however when I was looking at the outputs I was not taking the LoP into account and basically not recognizing that 180 is essentially the same angle as -180.
(I was also looking at the output in radians and just didn't see what should have been obvious)
Long story short, I have a bug I thought was in this area of the code and got lost in the weeds.
Seems I was wrong above. see OP for edge case.
Here's some code I used to test these,
I used variations of the following inputs:
pos = new Vector4() { X = 0.25, Y = 0.25 };
vel = new Vector4() { X = Distance.KmToAU(-25), Y = Distance.KmToAU(25) };
And tested them with the following
double parentMass = 1.989e30;
double objMass = 2.2e+15;
double sgp = GameConstants.Science.GravitationalConstant * (parentMass + objMass) / 3.347928976e33;
Vector4 ev = OrbitMath.EccentricityVector(sgp, pos, vel);
double e = ev.Length();
double specificOrbitalEnergy = Math.Pow(vel.Length(), 2) * 0.5 - sgp / pos.Length();
double a = -sgp / (2 * specificOrbitalEnergy);
double ae = e * a;
double aop = Math.Atan2(ev.Y, ev.X);
double eccentricAnomaly = OrbitMath.GetEccentricAnomalyFromStateVectors(pos, a, ae, aop);
double aopD = Angle.ToDegrees(aop);
double directAngle = Math.Atan2(pos.Y, pos.X);
var θ1 = OrbitMath.TrueAnomaly(sgp, pos, vel);
var θ2 = OrbitMath.TrueAnomaly(ev, pos, vel);
var θ3 = OrbitMath.TrueAnomalyFromEccentricAnomaly(e, eccentricAnomaly);
var θ4 = OrbitMath.TrueAnomalyFromEccentricAnomaly2(e, eccentricAnomaly);
var θ5 = OrbitMath.TrueAnomaly(pos, aop);
double angleΔ = 0.0000001; //this is the "acceptable" amount of error, really only the TrueAnomalyFromEccentricAnomaly() calcs needed this.
Assert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ1), angleΔ);
Assert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ2), angleΔ);
Assert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ3), angleΔ);
Assert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ4), angleΔ);
Assert.AreEqual(0, Angle.DifferenceBetweenRadians(directAngle, aop - θ5), angleΔ);
and the following to compare the angles:
public static double DifferenceBetweenRadians(double a1, double a2)
{
return Math.PI - Math.Abs(Math.Abs(a1 - a2) - Math.PI);
}
And eccentricity Vector found thus:
public static Vector4 EccentricityVector(double sgp, Vector4 position, Vector4 velocity)
{
Vector4 angularMomentum = Vector4.Cross(position, velocity);
Vector4 foo1 = Vector4.Cross(velocity, angularMomentum) / sgp;
var foo2 = position / position.Length();
return foo1 - foo2;
}
And EccentricAnomaly:
public static double GetEccentricAnomalyFromStateVectors(Vector4 position, double a, double linierEccentricity, double aop)
{
var x = (position.X * Math.Cos(-aop)) - (position.Y * Math.Sin(-aop));
x = linierEccentricity + x;
double foo = GMath.Clamp(x / a, -1, 1); //because sometimes we were getting a floating point error that resulted in numbers infinatly smaller than -1
return Math.Acos(foo);
}
Thanks to Futurogogist and Spektre for their help.
I am assuming you are working in two dimensions?
Two dimensional vectors of position p and velocity v. The constant K is the the product of the gravitational constant and the mass of the gravity generating body. Calculate the eccentricity vector
eccVector = (dot(v, v)*p - dot(v, p)*v) / K - p / sqrt(dot(p, p));
eccentricity = sqrt(dot(eccVector, eccVector));
eccVector = eccVector / eccentricity;
b = { - eccVector.y, eccVector.x}; //unit vector perpendicular to eccVector
r = sqrt(dot(p, p));
cos_TA = dot(p, eccVector) / r; \\ cosine of true anomaly
sin_TA = dot(p, b) / r; \\ sine of true anomaly
if (sin_TA >= 0) {
trueAnomaly = arccos(cos_TA);
}
else if (sin_TA < 0){
trueAnomaly = 2*pi - arccos(cos_TA);
}
I'm setting up an automatic system to be able to attach a sprite and it will gather all its colours and the world position of each sprite. A list/class of all the colours used has been set up but how would get the position of all these sprites?
I have already tried doing this mathematically like getting the complete size of the sprite and then working out the size of each pixel and then working out the position from that. But this seems flawed due to the position of the sprite possibly changing.
Sprite ColouredSpriteTexture = ColoredSprite.GetComponent<SpriteRenderer>().sprite;
Texture2D ColouredTexture = ColouredSpriteTexture.texture;
float XsizeF = ColoredSprite.transform.localScale.x;
int Xsize = (int)XsizeF;
float YsizeF = ColoredSprite.transform.localScale.y;
int Ysize = (int)YsizeF;
List<Color> TempList = new List<Color>();
//Could spawn pixels by getting x and y size and dividing them by 100 50/100 = 0.50f
//if the tile has a color then spawn pixel if not 0.50 += 0.50
//TODO test if this logic will work
float PixelSize = XsizeF / 100;
float currentPos = PixelSize;
for (int x = 0; x < Xsize; x++)
{
for (int y = 0; y < Ysize; y++)
{
int listAmount = TempList.Count;
Color ColoredTex = ColouredTexture.GetPixel(x, y);
float TextureAlpha = ColoredTex.a;
if (!TempList.Contains(ColoredTex) && TextureAlpha != 0)
{
TempList.Add(ColoredTex);
ColorByNumber tempColor = new ColorByNumber();
tempColor.Color = ColoredTex;
tempColor.ColorNumber = listAmount;
ColorOptions.Add(tempColor);
}
if(TextureAlpha == 1)
{
GameObject ColorPixel = Instantiate(PixelPrefab);
ColorPixel.transform.localScale = new Vector3(XsizeF, YsizeF, 0);
ColorPixel.transform.SetParent(this.transform);
ColorPixel.name = "Pixel (" + x.ToString() + "," + y.ToString() + ")";
}
}
}
All I would need is somehow each pixel returning its position so I can store this data and be able to spawn anything on top of this pixel.
I haven't had a chance to test this math yet so there may be some mistakes in it:
Every graphical image in Unity has a PPU, this and the object scale are going to be a huge factor. For argument sake I am going to clearly define these for 1 object.
Image dimensions : 128x128
PPU: 64
Scale: 1,1,1
Object Bounds: would
come from the renderer, which I am unsure if that bounds already
takes in account the scale(Most likely) however in the case you
cannot use that you can calculate the ObjectBoundsWidth or height
just by dividing the width or height of the texture by the PPU.
This should give you bounds of the texture in world space.
We are also going to make an assumption that we are only working on the X and Y axis and ignore the Z axis, if you want to use Z instead of Y then just make the necessary changes to be Z Scale and Z position and Z Bounds.
World position of a pixel located at 2,10. Per the documentation the pixel coordinates start at the lower left this means 0,0 is the bottom left corner, and 2,10 is 2 pixels left and 10 pixels up.
EDIT:
So I plugged all of this into a google sheet and determined the previous algorithm I provided was wrong here is the correct one in a pseudo code format
// This function takes in either the x or y, and the width or height of
// the bounds, then the x or y position of the object attached to.
// It also assumes the pivot is the center of the sprite.
float CalculateWorldPosOfPixelCoordinate(int coord, float boundsSize, float position, float scale)
{
float PixelInWorldSpace = 1.0f / PPU;
float startPos= position - (boundsSize* 0.5f * scale);
return startPos + (PixelInWorldSpace * coord) * scale;
}
This is using objectBounds we determined ourselves that is why we are multiply by scale.
this would give use a world position of: -0.97, -0.84
The algorithm i believe is the same for Y, just replace the coord with the Y position, and the bounds with the height instead of the width.
Like I said this could be wrong as I havent had a chance to test it, this also does not account for rotation either.
I have three vertices of a triangle i.e. (x1,y1,z1); (x2,y2,z2) and (x3,y3,z3).
The bounding box of my triangle is a cube of length = Maximum(xmax-xmin, ymax-ymin,zmax-zmin). xmax,xmin,....,zmin can be calculated by looping through all the vertices of the triangle.
Now,considering a particular resolution size(h), I divide my bounding box into grids.For example,if my bounding box is of length 10 and resolution is 1,No. of grids will be 1000(10*10*10).
Now,I want to find out all those grids(cubes) which are intersected by my Triangle as well as those cubes,which lie inside my triangle.
I am following the below approach:
-> Storing all the grids of my bounding box in a list (using 3 "for" loops for x,y,z.This involves huge memory wastage)
-> I am then looping through each grid coordinate in my list,checking out if the cube lies on my plane,if the cube lines on my plane,then I am checking if my grid is intersected by three edges of my triangle (or) if my grid is located inside my triangle.
I am using the following algorithms for checking the intersection and inside criteria:
bool IfLineIntersectsPoint(float x, float y, float z)
{
bool checkifIntersects = false;
FindProjectedPointonPlane(x, y, z);
//Px,Py and Pz are projected points on the plane
if ((((Px - vertex1x) / a) == ((Py - vertex1y) / b)) && (((Px - vertex1x) / a) == ((Pz - vertex1z) / c)))
{
checkifIntersects = true;
}
return checkifIntersects;
}
bool PointInTriangle(Vector3[] TriangleVectors, Vector3 P)
{
Vector3 A = TriangleVectors[0], B = TriangleVectors[1], C = TriangleVectors[2];
if (SameSide(P, A, B, C) && SameSide(P, B, A, C) && SameSide(P, C, A, B))
{
Vector3 AB = Vector3.Subtract(A, B);
Vector3 AC = Vector3.Subtract(A, C);
Vector3 AP = Vector3.Subtract(A, P);
Vector3 vc1 = Vector3.Cross(AB, AC);
float magnitude1 = AB.Length();
float magnitude2 = vc1.Length();
Vector3 NormAP = new Vector3(AP.X / magnitude1, AP.Y / magnitude1, AP.Z / magnitude1);
Vector3 NormVC1 = new Vector3(vc1.X / magnitude2, vc1.Y / magnitude2, vc1.Z / magnitude2);
float ftw = Math.Abs(Vector3.Dot(NormAP, NormVC1));
if (ftw <= 0.1f)
return true;
}
return false;
}
I would be really glad,if someone can suggest any changes in my algorithm and the above two functions,so as to minimize my computation time. Also,if I have some 8-9 triangles,Everytime,I am checking all these criteria for all 1000 grids.Can I get some subset(some 100-150 grids) of these 1000 grids and proceed?
Thanks in Advance.
I am writing a program in which I need to draw polygons of an arbitrary number of sides, each one being translated by a given formula which changes dynamically. There is some rather interesting mathematics involved but I am stuck on this probelm.
How can I calculate the coordinates of the vertices of a regular polygon (one in which all angles are equal), given only the number of sides, and ideally (but not neccessarily) having the origin at the centre?
For example: a hexagon might have the following points (all are floats):
( 1.5 , 0.5 *Math.Sqrt(3) )
( 0 , 1 *Math.Sqrt(3) )
(-1.5 , 0.5 *Math.Sqrt(3) )
(-1.5 , -0.5 *Math.Sqrt(3) )
( 0 , -1 *Math.Sqrt(3) )
( 1.5 , -0.5 *Math.Sqrt(3) )
My method looks like this:
void InitPolygonVertexCoords(RegularPolygon poly)
and the coordinates need to be added to this (or something similar, like a list):
Point[] _polygonVertexPoints;
I'm interested mainly in the algorithm here but examples in C# would be useful. I don't even know where to start. How should I implement it? Is it even possible?!
Thank you.
for (i = 0; i < n; i++) {
printf("%f %f\n",r * Math.cos(2 * Math.PI * i / n), r * Math.sin(2 * Math.PI * i / n));
}
where r is the radius of the circumsribing circle. Sorry for the wrong language No Habla C#.
Basically the angle between any two vertices is 2 pi / n and all the vertices are at distance r from the origin.
EDIT:
If you want to have the center somewher other than the origin, say at (x,y)
for (i = 0; i < n; i++) {
printf("%f %f\n",x + r * Math.cos(2 * Math.PI * i / n), y + r * Math.sin(2 * Math.PI * i / n));
}
The number of points equals the number of sides.
The angle you need is angle = 2 * pi / numPoints.
Then starting vertically above the origin with the size of the polygon being given by radius:
for (int i = 0; i < numPoints; i++)
{
x = centreX + radius * sin(i * angle);
y = centreY + radius * cos(i * angle);
}
If your centre is the origin then simply ignore the centreX and centreY terms as they'll be 0,0.
Swapping the cos and sin over will point the first point horizontally to the right of the origin.
Sorry, I dont have a full solution at hand right now, but you should try looking for 2D-Rendering of Circles. All classic implementations of circle(x,y,r) use a polygon like you described for drawing (but with 50+ sides).
Say the distance of the vertices to the origin is 1. And say (1, 0) is always a coordinate of the polygon.
Given the number of vertices (say n), the rotation angle required to position the (1, 0) to the next coordinate would be (360/n).
The computation required here is to rotate the coordinates. Here is what it is; Rotation Matrix.
Say theta = 360/n;
[cos(theta) -sin(theta)]
[sin(theta) cos(theta)]
would be your rotation matrix.
If you know linear algebra you already know what i mean. If dont just have a look at Matrix Multiplication
One possible implementation to generate a set of coordinates for regular polygon is to:
Define polygon center, radius and first vertex1. Rotate the vertex n-times2 at an angle of: 360/n.
In this implementation I use a vector to store the generated coordinates and a recursive function to generate them:
void generateRegularPolygon(vector<Point>& v, Point& center, int sidesNumber, int radius){
// converted to radians
double angRads = 2 * PI / double(sidesNumber);
// first vertex
Point initial(center.x, center.y - radius);
rotateCoordinate(v, center, initial, angRads, sidesNumber);
}
where:
void rotateCoordinate(vector<Point>& v, Point& axisOfRotation, Point& initial, double angRads, int numberOfRotations){
// base case: number of transformations < 0
if(numberOfRotations <= 0) return;
else{
// apply rotation to: initial, around pivot point: axisOfRotation
double x = cos(angRads) * (initial.x - axisOfRotation.x) - sin(angRads) * (initial.y - axisOfRotation.y) + axisOfRotation.x;
double y = sin(angRads) * (initial.x - axisOfRotation.x) + cos(angRads) * (initial.y - axisOfRotation.y) + axisOfRotation.y;
// store the result
v.push_back(Point(x, y));
rotateCoordinate(v, axisOfRotation, Point(x,y), angRads, --numberOfRotations);
}
}
Note:
Point is a simple class to wrap the coordinate into single data structure:
class Point{
public:
Point(): x(0), y(0){ }
Point(int xx, int yy): x(xx), y(yy) { }
private:
int x;
int y;
};
1 in terms of (relative to) the center, radius. In my case the first vertex is translated from the centre up horizontally by the radius lenght.
2 n-regular polygon has n vertices.
The simple method is:
Let's take N-gone(number of sides) and length of side L. The angle will be T = 360/N.
Let's say one vertices is located on origin.
* First vertex = (0,0)
* Second vertex = (LcosT,LsinT)
* Third vertex = (LcosT+Lcos2T, LsinT+Lsin2T)
* Fourth vertex = (LcosT+Lcos2T+Lcos3T, LsinT+Lsin2T+Lsin3T)
You can do in for loop
hmm if you test all the versions that are listed here you'll see that the implementation is not good. you can check the distance from the center to each generated point of the polygon with : http://www.movable-type.co.uk/scripts/latlong.html
Now i have searched a lot and i could not find any good implementation for calculating a polyogon using the center and the radius...so i went back to the math book and tried to implement it myself. In the end i came up with this...wich is 100% good:
List<double[]> coordinates = new List<double[]>();
#region create Polygon Coordinates
if (!string.IsNullOrWhiteSpace(bus.Latitude) && !string.IsNullOrWhiteSpace(bus.Longitude) && !string.IsNullOrWhiteSpace(bus.ListingRadius))
{
double lat = DegreeToRadian(Double.Parse(bus.Latitude));
double lon = DegreeToRadian(Double.Parse(bus.Longitude));
double dist = Double.Parse(bus.ListingRadius);
double angle = 36;
for (double i = 0; i <= 360; i += angle)
{
var bearing = DegreeToRadian(i);
var lat2 = Math.Asin(Math.Sin(lat) * Math.Cos(dist / earthRadius) + Math.Cos(lat) * Math.Sin(dist / earthRadius) * Math.Cos(bearing));
var lon2 = lon + Math.Atan2(Math.Sin(bearing) * Math.Sin(dist / earthRadius) * Math.Cos(lat),Math.Cos(dist / earthRadius) - Math.Sin(lat) * Math.Sin(lat2));
coordinates.Add(new double[] { RadianToDegree(lat2), RadianToDegree(lon2) });
}
poly.Coordinates = new[] { coordinates.ToArray() };
}
#endregion
If you test this you'll see that all the points are at the exact distance that you give ( radius ). Also don't forget to declare the earthRadius.
private const double earthRadius = 6371.01;
This calculates the coordinates of a decagon. You see the angle used is 36 degrees. You can split 360 degrees to any number of sides that you want and put the result in the angle variable.
Anyway .. i hope this helps you #rmx!
I am trying to translate an OpenGl object around in a helical pattern. I cannot figure this out. Problem is I know I need to increment the angle for the x, y, and z coordinates, but the translate function that I use only moves the object by a translate amount which is specific to the object. The Axis I am using is Y up, Z toward the screen and X to the right.
public override void Move(Figure fig)
{
double angle = 0;
double x = RADIUS * Math.Cos(angle);
double y = (angle / RADIUS);
double z = RADIUS * Math.Sin(angle);
fig.Translate(x, y, z);
angle += .5;
}
public void Translate(double fx, double fy, double fz)
{
translateAmt[0] += fx;
translateAmt[1] += fy;
translateAmt[2] += fz;
}
Here are two ways you could approach this:
Procedurally
Check out the ProcessHelix function in NeHe Lesson 36. A little bit hard to read but you should be able to see the basic loop and calculations used to get the points along a helix.
2 Translations and a Rotation
If you perform these transformations in the proper order you can get the helical motion. This is the order you would imagine doing it in your head:
Translate the object away from the origin (e.g. +x) the radius of your helix
Rotate the object around the origin (y axis), creating circular motion
Translate the object along the y axis, creating helical motion.
So in OpenGL, you'd do those backwards, as the last matrix specified is the first one applied... translate in +y (time dependent), rotate around y (time dependent), and translate in x.
Got it working!
private const double RADIUS = 1;
private const double INTERVAL = 0.1;
private double theta = 5;
private double alpha = 0;
private const double ANGLE = 10;
public override void Move(Figure fig)
{
double x = RADIUS * Math.Cos(theta);
double y = 0;
double z = RADIUS * Math.Sin(theta);
double deltaX = z * Math.Cos(alpha) - x * Math.Sin(alpha);
double deltaZ = x * Math.Cos(alpha) + z * Math.Sin(alpha);
fig.Translate(deltaX, y, deltaZ);
fig.Rotate(ANGLE, 0, 0, 1);
alpha += INTERVAL;
}
I think you are missing some code.
In move, angle always starts with zero, so the x,y,z values will always be the same, as the next time you go into Move it will be zero again.
You should be passing in the angle, perhaps, into Move, so that this value will continue to change.
You may need to pass it in as a pointer so that you can update it within the function and have it actually be updated, or, have Move return a double and return angle;.
I expect that your changing of the angle by 0.5 isn't correct, it may need to be based on the repetition number * some value, but you may want to fix your first problem first.