I have a projectile that I would like to pass through specific coordinates at the apex of its path. I have been using a superb equation that giogadi outlined here, by plugging in the velocity values it produces into chipmunk's cpBodyApplyImpulse function.
The equation has one drawback that I haven't been able to figure out. It only works when the coordinates that I want to hit have a y value higher than the cannon (where my projectile starts). This means that I can't shoot at a downward angle.
Can anybody help me find a suitable equation that works no matter where the target is in relation to the cannon?
As pointed out above, there isn't any way to make the apex be lower than the height of the cannon (without making gravity work backwards). However, it is possible to make the projectile pass through a point below the cannon; the equations are all here. The equation you need to solve is:
angle = arctan((v^2 [+-]sqrt(v^4 - g*(x^2+2*y*v^2)))/g*x)
where you choose a velocity and plug in the x and y positions of the target - assuming the cannon is at (0,0). The [+-] thing means that you can choose either root. If the argument to the square root function is negative (an imaginary root) you need a larger velocity. So, if you are "in range" you have two possible angles for any particular velocity (other than in the maximum range 45 degree case where the two roots should give the same answer).
I suspect one trajectory will tend to 'look' much more sensible than the other, but that's something to play around with once you have something working. You may want to stick with the apex grazing code for the cases where the target is above the cannon.
Related
I am trying to create edges with bends for a layout. Normally, I am using a haystack edge in the graph but whenever an edge bend has to be created, the curve-style of the edge is changed to segments. Currently, I am only creating edges with single bends. I have tried the code provided in this post but it is not creating proper edges. Currently, I am using the code from cytoscape.js-edge-editing, since it is creating better results.
The main problem is that the segment-distances values which cause the bendpoint to be created at the wrong location. Since, the functions in the above provided codes are not creating proper bendpoints, what is the right way to go about this?
A sample problem is as shown:
An edge bend has to created created in the edge from n12 to n15 where n12 is the source. The values of segment-distances and segment-weights are shown in the console. Having a positive value of segment-distances creates the bendpoint at the wrong position. It was actually supposed to be to the right of n12 and to the top of n15.
Whereas in another scenario, as shown in the following figure, an edge bend has to be created in the edge from n3 and n2. And the positions of these nodes are quite similar to n12 and n15 wrt each other. Their edge is given the same values of segment-distances and segment-weights as for the edge in the previous figure. And yet, the bendpoint is created (not accurately) but almost near to the expected location. Whereas the same value of segment-distance creates the bendpoint at the opposite location in the previous scenario.
I do not understand why this is happening. Can someone please guide me as how to solve this problem?
Refer to edge-distances:
edge-distances : With value intersection (default), the line from source to target for segment-weights is from the outside of the source node’s shape to the outside of the target node’s shape. With value node-position, the line is from the source position to the target position. The node-position option makes calculating edge points easier — but it should be used carefully because you can create invalid points that intersection would have automatically corrected.
https://js.cytoscape.org/#style/segments-edges
The intersection point is different from the node centre point (position).
If you want right-angled edges, you should probably just use taxi edges: https://js.cytoscape.org/#style/taxi-edges
I am trying to model the interior of an epithelial space and am stuck on movement around the interior edges of a cylindrical space. Basically, I'm trying to implement StickyBorders and keep agents on those borders in a cylindrical space that I am creating.
Is there a way to use cylindrical coordinates in Repast Simphony? I found this example (https://www.researchgate.net/publication/259695792_An_Agent-Based_Model_of_Vascular_Disease_Remodeling_in_Pulmonary_Arterial_Hypertension) where they seem to have done something similar, but the paper doesn't explain methods in much depth, and I don't believe this is an example in the repast simphony models.
Currently, I have a class of epithelial cells that are set up to form a cylinder and other agents start just inside that cylinder. To move, they are choosing their most desired spot (similar to the Zombie code) then pointing to a new location in the direction of that desired location within one grid square of that original location. They check that new point before moving to it and make sure that there are at least two other epithelial cells in the immediate moore neighborhood, to ensure they stay against the wall.
GridPoint intendedpt = new GridPoint((int)Math.rint(alongX),(int)Math.rint(alongY),(int)Math.rint(alongZ));
GridCellNgh<EpithelialCell> nearEpithelium = new GridCellNgh<EpithelialCell>(mac_grid, intendedpt, EpithelialCell.class, 1,1,1);
List<GridCell<EpithelialCell>> EpiCells = nearEpithelium.getNeighborhood(false);
int nearbyEpiCellsCount=0;
for (GridCell<EpithelialCell> cell: EpiCells) {
nearbyEpiCellsCount++;
}
if (nearbyEpiCellsCount<2) {
System.out.println(this + " leaving epithelial wall /r");
RunEnvironment.getInstance().pauseRun();
//TODO: where to go if false
}
I am wondering if there is a way to either set the boundaries of the space to be a cylinder or to check which side of the agent is against the wall and restrict its movement in that direction.
The sticky border code (StickyBorders.java) essentially just checks if the point that the agent moves to is beyond any of the space's dimensions, and if so the point is clamped to that dimension. So, for example, if the space is 3x4 and an agent's movement would take it to 4,2, then that point becomes 3,2 and the agent is placed there. Can you do something like that in this case? If not, can you edit your question to explain why not and maybe that will help us understand better.
The approach we took in that model was to use a 3D grid space with custom borders and query methods. The space itself was still Cartesian - we just visualized it as a cylinder using custom display code. Using the Cartesian grid was an reasonable approximation for this application since the cell dimensions were significantly smaller that the vessel radius, so curvature effects were neglected. The boundary conditions on the vessel space were wrap around in the angular dimension, so that cells could move continuously around the circumference of the vessel, and the axial boundary conditions were also wrapped, as we assumed a long enough vessel length that this would be reasonable. The wall thickness dimension had hard boundaries at the basement membrane (y=0) and at the fluid interface (y=wall thickness).
Depending on which type of space you are using, you will need to implement a PointTranslator or GridPointTranslator that performs the border functions. If you want specific examples of the code I suggest you reach out to the author's directly.
I'm trying to build a MKPolygon using the outer boundary of a set of coordinates.
From what I can tell, there is no delivered functionality to achieve this in Xcode (the MKPolygon methods would use all points to build the polygon, including interior points).
After some research I've found that a convex-hull solves this problem.
After looking into various algorithms, the one I can best wrap my head around to implement is QuickHull.
This takes the outer lat coords and draws a line between the two. From there, you split your points based on that line into two subsets and process distance between the outer lats to start building triangles and eliminating points within until you are left with the outer boundary.
I can find the outer points just by looking at min/max lat and can draw a line between the two (MKPolyline) - but how would I determine whether a point falls on one side or the other of this MKPolyline?
A follow up question is whether there is a hit test to determine whether points fall within an MKPolygon.
Thanks!
I ended up using a variation of the gift wrap algorithm. Certainly not a trivial task.
Having trouble with formatting of the full code so I'll have to just put my steps (probably better because I have some clean up to do!)
I started with an array of MKPointAnnotations
1) I got the lowest point that is furthest left. To do this, I looped through all of the points and compared lat/lng to get lowest point. This point will definitely be in the convex hull, so add it to a NSMutableArray that will store our convex hull points (cvp)
2) Get all points to the left of the lowest point and loop through them, calculating the angle of the cvp to the remaining points on the left. Whichever has the greatest angle, will be the point you need to add to the array.
atan(cos(lat1)sin(lat2)-sin(lat1)*cos(lat2)*cos(lon2-lon1), sin(lon2-lon1)*cos(lat2))
For each point found, create a triangle (by using lat from new point and long from previous point) and create a polygon. I used this code to do a hit test on my polygon:
BOOL mapCoordinateIsInPolygon = CGPathContainsPoint(polygonView.path, NULL, polygonViewPoint, NO);
If anything was found in the hit test, remove it from the comparison array (all those on the left of the original array minus the hull points)
Once you have at least 3 points in your cvp array, build another polygon with all of the cvp's in the array and remove anything within using the hit test.
3) Once you've worked through all of the left points, create a new comparison array of the remaining points that haven't been eliminated or added to the hull
4) Use the same calculations and polygon tests to remove points and add the cvp's found
At the end, you're left with a list of points in that make up your convex hull.
I have several boxes (x,y,width,height) randomly scattered around, and some of them need to be linked from point (x1,y1) in box1 to point (x2,y2) in box2 by drawing a line. I am trying to figure a way to make such line avoid passing through any other boxes (other than box1 and box2) by drawing several straight interconnected lines to go around any box in the way (if it is not possible to go with one straight line). The problem is that I don't know an algorithm for such thing (let alone having a technical/common name for it). Would appreciate any help in the form of algorithm or expressed ideas.
Thanks
Assuming that the lines can't be diagonal, here's one simple way. It's based on BFS and will also find the shortest line connecting the points:
Just create a graph, containing one vertex for each point (x, y) and for each point the edges:
((x,y),(x+1,y)) ((x,y),(x-1,y)) ((x,y),(x,y+1)) ((x,y),(x,y-1))
But each of this edges must be present only if it doesn't overlap a box.
Now just do a plain BFS from point (x1,y1) to (x2,y2)
It's really easy to obtain also diagonal lines the same way but you will need 8 edges for each vertex, that are, in addition to the previouses 4:
((x,y),(x-1,y+1)) ((x,y),(x-1,y-1)) ((x,y),(x+1,y-1)) ((x,y),(x+1,y+1))
Still, each edge must be present only if it doesn't overlap a box.
EDIT
If you can't consider space divided into a grid, here's another possibility, it won't give you the very shortest path, though.
Create a graph, in which each box is a vertex and has an edge to any other box that can be reached without the line to overlap a third box. Now find the shortet path using dijkstra between box1 and box2 containing the two points.
Now consider each box to have a small countour that doesn't overlap any other box. This way you can link the entering and the exiting point of each box in the path found through dijistra, passing through the countour.
Put all (x,y) coords of the corners of the boxes in a set V
Add the start- and end coordinates to V.
Create a set of edges E connecting each corner that does not cross any box-side (except for the diagonals in the boxes).
How to check if a line crosses a box side can be done with this algorithm
Now use a path-finding algorithm of your choice, to find a path in the graph (V, E).
If you need a simple algorithm that finds the shortest path, just go with a BFS.
(This will produce a path that goes along the sides of some boxes. If this is undesirable, you could in step 1 put the points at some distance delta from the actual corners.)
If the edges may not be diagonal:
Create a large grid of lines that goes between the boxes.
Throw away the grid-edges that cross a box-side.
Find a path in the grid using a path-finding algorithm of your choice.
I have a game I am working on that has homing missiles in it. At the moment they just turn towards their target, which produces a rather dumb looking result, with all the missiles following the target around.
I want to create a more deadly flavour of missile that will aim at the where the target "will be" by the time it gets there and I am getting a bit stuck and confused about how to do it.
I am guessing I will need to work out where my target will be at some point in the future (a guess anyway), but I can't get my head around how far ahead to look. It needs to be based on how far the missile is away from the target, but the target it also moving.
My missiles have a constant thrust, combined with a weak ability to turn. The hope is they will be fast and exciting, but steer like a cow (ie, badly, for the non HitchHiker fans out there).
Anyway, seemed like a kind of fun problem for Stack Overflow to help me solve, so any ideas, or suggestions on better or "more fun" missiles would all be gratefully received.
Next up will be AI for dodging them ...
What you are suggesting is called "Command Guidance" but there is an easier, and better way.
The way that real missiles generally do it (Not all are alike) is using a system called Proportional Navigation. This means the missile "turns" in the same direction as the line-of-sight (LOS) between the missile and the target is turning, at a turn rate "proportional" to the LOS rate... This will do what you are asking for as when the LOS rate is zero, you are on collision course.
You can calculate the LOS rate by just comparing the slopes of the line between misile and target from one second to the next. If that slope is not changing, you are on collision course. if it is changing, calculate the change and turn the missile by a proportionate angular rate... you can use any metrics that represent missile and target position.
For example, if you use a proportionality constant of 2, and the LOS is moving to the right at 2 deg/sec, turn the missile to the right at 4 deg/sec. LOS to the left at 6 deg/sec, missile to the left at 12 deg/sec...
In 3-d problem is identical except the "Change in LOS Rate", (and resultant missile turn rate) is itself a vector, i.e., it has not only a magnitude, but a direction (Do I turn the missile left, right or up or down or 30 deg above horizontal to the right, etc??... Imagine, as a missile pilot, where you would "set the wings" to apply the lift...
Radar guided missiles, which "know" the rate of closure. adjust the proportionality constant based on closure (the higher the closure the faster the missile attempts to turn), so that the missile will turn more aggressively in high closure scenarios, (when the time of flight is lower), and less aggressively in low closure (tail chases) when it needs to conserve energy.
Other missiles (like Sidewinders), which do not know the closure, use a constant pre-determined proportionality value). FWIW, Vietnam era AIM-9 sidewinders used a proportionality constant of 4.
I've used this CodeProject article before - it has some really nice animations to explain the math.
"The Mathematics of Targeting and Simulating a Missile: From Calculus to the Quartic Formula":
http://www.codeproject.com/KB/recipes/Missile_Guidance_System.aspx
(also, hidden in the comments at the bottom of that article is a reference to some C++ code that accomplishes the same task from the Unreal wiki)
Take a look at OpenSteer. It has code to solve problems like this. Look at 'steerForSeek' or 'steerForPursuit'.
Have you considered negative feedback on the recent change of bearing over change of time?
Details left as an exercise.
The suggestions is completely serious: if the target does not maneuver this should obtain a near optimal intercept. And it should converge even if the target is actively dodging.
Need more detail?
Solving in a two dimensional space for ease of notation. Take \vec{m} to be the location of the missile and vector \vec{t} To be the location of the target.
The current heading in the direction of motion over last time unit: \vec{h} = \bar{\vec{m}_i - \vec{m}_i-1}}. Let r be the normlized vector between the missile and the target: \vec{r} = \bar{\vec{t} - \vec{m}}. The bearing is b = \vec{r} \dot \vec{h} Compute the bearing at each time tick, and the change thereof, and change heading to minimize that quantity.
The math is harrier in 3d because of the need to find the plane of action at each step, but the process is the same.
You'll want to interpolate the trajectory of both the target and the missile as a function of time. Then look for the times in which the coordinates of the objects are within some acceptable error.