Math - Displaying multiple objects in a single view using trigonometry - c#

It might be that my math is rusty or I'm just stuck in my box after trying to solve this for so long, either way I need your help.
Background: I'm making a 2d-based game in C# using XNA. In that game I want a camera to be able to zoom in/out so that a certain part of objects always are in view. Needless to say, the objects move in two dimensions while the camera moves in three.
Situation: I'm currently using basic trigonometry to calculate which height the camera should be at for all objects to show. I also position the camera between those objects.
It looks something like this:
1.Loop through all objects to find the outer edges of our objects : farRight, farLeft, farUp, farDown.
2.When we know what the edges of what has to be shown are, calculate the center, also known as the camera position:
CenterX = farLeft + (farRight - farLeft) * 0.5f;
CenterY = farUp + (farDown - farUp) * 0.5f;
3.Loop through our edges to find the largest value compared to our camera position, thus the furthest distance from the center of screen.
4.Using the largest distance-value we can easily calculate the needed height to show all of those objects (points):
float T = 90f - Constants.CAMERA_FIELDOFVIEW * 0.5f;
float height = (float)Math.Tan(MathHelper.ToRadians(T)) * (length);
So far so good, the camera positions itself perfectly based on the calculations.
Problem:
a) My rendering target is 1280*720 with a Field of View of 45 degrees, so one always sees a bit more on the X-axis, 560 pixels more actually. This is not a problem per se but more one that on b)...
b) I want the camera to be a bit further out than it is, so that one sees a bit more on what is happening beyond the furthest point. Sure, this happens on the X-axis, but that is technically my flawed logic's result. I want to be able to see more on both the X- and Y-axis and to control this behavior.
Question
Uhm, so to clarify. I would like to have some input on a way to make the camera position itself, creating this state:
Objects won't get closer than say... 150 pixels to the edge of the X-axis and 100 pixels to the edge of the Y-axis. To do this the camera shall position itself along the Z-axis so that the field of view covers it all.
I don't need help with the coding, just the math and logic of calculating the height of my camera. As you probably can see, I have a hard time wrapping this inside my head and even harder time trying to explain it to you.
If anyone out there has been dealing with this or is just better than me at math, I'd appreciate whatever you have to say! :)

Don't you just need to add or subtract 150 or 100 pixels (depending on which edge you are looking at) to each distance measurement in your loop at step 3 and carry this larger value into length at step 4? Or am I missing something.

I can't explore this area further at the moment, but if anyone is having the same issue but is not satisfied by provided answer there is another possibility in XNA.
ViewPort.Unproject()
This nifty feature converts a screen space coordinate to a world space one.
ViewPort.Project()
Does the opposite thing, namely converting world space to screen space. Just thought that someone might want to go further than me. As much as my OCD hates to leave things not perfect, I can't be perfectioning this... yet.

Related

Sphere vs Rotation Box Custom Collision Problem (C#, Unity)

I'm not really like to post questions about problems without doing the research, but I'm close to give up, so I thought I give it a shot and ask you about my problem.
I want to create a custom collision detection in Unity ( So please don't advice "use rigidbody and\or colliders" because I don't want to use them by purpose).
The main idea: I want to detect Basic Sphere and Basic Box collision. I already find AABB vs Sphere theme with the following solution:
bool intersect(sphere, box) {
var x = Math.max(box.minX, Math.min(sphere.x, box.maxX));
var y = Math.max(box.minY, Math.min(sphere.y, box.maxY));
var z = Math.max(box.minZ, Math.min(sphere.z, box.maxZ));
var distance = Math.sqrt((x - sphere.x) * (x - sphere.x) +
(y - sphere.y) * (y - sphere.y) +
(z - sphere.z) * (z - sphere.z));
return distance < sphere.radius;
}
And this code does the job, the box bounding and the sphere center point with radius works fine, I can detect the Sphere collision on Box.
The problem is, I want to Rotating the Cube in Runtime, so that will screw up everything, the bounding will split away and the collision will gone (or collide on random places). I've read about some comments where they said, bounding not works with rotation, but I'm not sure what else can I use to solve this problem.
Can you help me with this topic please? I'll take every advice I can get (except Colliders & Rigidbodies of course).
Thank you very much.
You might try using the separating axis theorem. Essentially, for a polyhedron, you use the normal of each face to create an axis. Project the two shapes you are comparing onto each axis and look for an intersection. If there is no intersection along any of the axes, there is no intersection of shapes. For a sphere, you will just need to project onto the polyhedron's axes. There is a great 2D intro to this from metanet.
Edit: hey, check it out-- a Unity implementation.
A good method to find if an AABB (axis aligned bounding box) and sphere are intersecting is to find the closest point on the box to the sphere's center and determine if that point is within the sphere's radius. If so, then they are intersecting, if not then not.
I believe you can do the same thing with this more complicated scenario. You can represent a rotated AABB with a geometrical shape called a parallelepiped. You would then find the closest point on the parallelepiped to the center of the sphere and again check if that point exists within the sphere's radius. If so, then they intersect. If not, then not.
The difficult part is finding the closest point on the parallelepiped. You can represent a parallelepiped in code with 4 3d vectors: center, extentRight, extentUp, and extentForward. This is similar to how you can represent an AABB with a 3d vector for center along with 3 floats: extentRight, extentUp, and extentForward. The difference is that for the parallelepiped those 3 extents are not 1 dimensional scalars, but are full vectors.
When finding the closest point on an AABB surface to a given point, you are basically taking that given point and clamping it to the AABB's volume. You would, for example, call Math.Clamp(point.x, AABB.Min.x, AABB.Max.x) and so on for Y and Z.
The resulting X,Y,Z would be the closest point on the AABB surface to the given point.
To do this for a parallelepiped you need to solve the "linear combination" (math keyword) of extentRight(ER), extentUp(EU), and extentForward(EF) to get the given point. In other words, what scalars do you have to multiply ER, EU, and EF by to get to the given point? When you find those scalars you need to clamp them between 0 and 1 and then multiply them again by ER, EU, and EF respectively to get that closest point on the surface of the parallelepiped. Be sure to offset the given point by the Parallelepiped's min position so that the whole calculation is done in its local space.
I didn't want to spend any extra time learning how to solve for a linear combination (it seems it involves things like using an "augmented matrix" and "gaussian elimination") otherwise I'd include that here too. This should get you or anyone else reading this off to the right track hopefully.
Edit:
Actually I think its a lot simpler and you don't need a parallelepiped. If you have access to the rotation (Vector3 or Quaternion) that rotated the cube you could get the inverse of that and use that inverse rotation to orbit the sphere around the cube so that the new scenario is just the normal axis aligned cube and the orbited sphere. Then you can do a normal AABB - sphere collision detection.

How to rotate objects in OpenGL relative to local or global axes

I'm asking a question that has been asked a million times before, but I still haven't found a good answer after going through these and also resorting to other sites:
How to rotate a graphic over global axes, and not to local axes?
rotating objects in opengl
How to rotate vertices exactly like with glRotatef() in OpenGL?
Rotate object about 3 axes in OpenGL
Rotate an object on its own axes in OpenGL
Is it possible to rotate an object around its own axis and not around the base coordinate's axis?
OpenGL Rotation - Local vs Global Axes
Task is relatively simple, I am making an sensor module with accelerometer and gyro onboard, and I need to display rotation.
I have a 3D model of the object in STL format, I've made an STL parser and I can visualise the object perfectly well.
When I try to rotate it I get all kinds of strange results.
I am using SharpGL (the Scene component).
I tried to write an "effect" that (for now) is controlled with 3 separate trackbars, but this will be the data from the sensors.
I wanted to do it as an effect because (in theory) I could have more objects in the scene and I only need to rotate a specific one (and also for educational purposes as I am relatively new to OpenGL).
I tried to rotate the object using quaternions, multiplying them and generating a rotation matrix, then applying gl.MultMatrix(transformMatrix.AsColumnMajorArray).
I also tried gl.Rotate(angleX, 1, 0, 0) (and similar for Y and Z axes).
Depending on the order of quaternion multiplication or gl.Rotate(...) statements, I would get the object to rotate about the local axis (first), something weird (second), and the "world" third. For example, if I did it with quaternions qX*qY*qZ and got the rotation matrix from that, I would get (I think) the rotations about a local X, "arbitrary" Y, and the world Z axes.
The part I cannot understand is that when I apply gl.Rotate(dx, 1, 0, 0) (and others for Y and Z rotations) inside the trackbar's Scroll event, the entire scene rotates about the X, Y, and Z axes and in that order, and exactly as I expected the rotation to happen.
My only issue with this approach is that the entire scene rotates. So if I (hypothetically) wanted to draw a room around the object, the whole room would rotate too, which is not what I want.
I will post any code requested, but I feel there is too much and the aforementioned links have similar code to what I have.
At the end of the day, I want my object (Polygon in SharpGL terms) to rotate about its own axes (or about the "world" axes, but be consistent).
EDIT:
I've placed the project in my dropbox: https://goo.gl/1LzNhn
If someone wants to look at it, any help will be greatly appreciated.
In the MainForm, the TbRotXYZScroll function has trackbar code and the Rotation class is where the problem resides (or so I think).
Rotate X, Y, and Z by say 45 degrees in that order. All seems to work great. Now rotate X, Y, and Z further by another 30 or so degrees, try to visualise about which axis the rotation is happening as you rotate...
X seems to be always world and Z seems to be always local, while Y is something in between (changing the order of rotation changes this).
Going into TbRotXYZScroll function and changing method to 2 does what I want (except the rotation of the entire scene). Tried quaternions and they produce the exact same result, so I must be doing something wrong...
Changing it to 1 produces similar result, but that is applying the rotation to the polygons alone (not what's being rendered as that includes local coordinate axes too).
At the end of the day, I want my object (Polygon in SharpGL terms) to
rotate about its own axes (or about the "world" axes, but be
consistent).
I think this answer you put in your question is somehow explaining the situation. In order to perform rotation around object axis:
1. Perform Translation/Rotation to your object and make the object axis overlap with one of base axis (x,y or z)
2. Perform your rotation
3. Revert your object back to its original position. (simply revert the translation/rotations at step1)
Note: While doing that, one thing you should consider is openGL apply transformations from the reverse order.
Example :
glRotatef(90,1,0,0);
glTranslatef(-5,-10,5);
drawMyObject();
In this case, opengl will first translate your object and then rotate. So while writing your transformations consider that. Here is my answer that may give you an idea.

Draw travel distance in XNA 4

So basically i am creating an XNA game at college and i need some help with something as i cannot seem to figure it out myself and i'm pretty new to this.
Basically i have a spaceship with a scrolling background of stars. I have falling asteroids and basically the point of my game is to travel as far as possible without being hit by said asteroids.
I'm really looking for some guidance as to how i could measure a theoretical distance travelled by the ship and then draw it on screen?
Any help would be greatly appreciated.
Many thanks.
Solution A
Somewhere in your code you are defining the offset of the backdrop for each frame. You could just invert* this value and add it to the total amount every frame:
totalDistance += -backdropOffset;
If the offset is defined in pixels you have to convert it to your game world unit (kilometers, lightyears, ...) before displaying the distance.
* If the ship moves forward, the backdrop "slides" in the other direction.
Solution B (more work but less headaches)
It is actually not the backdrop that is moving; it's the ship. So why not move the ship and follow it with the camera?
You will be able to do all kinds of motion. Right now you have to invert every movement of the ship and then apply it to the backdrop. Kind of counter-intuitive, don't you think? So going with this solution your code will be much closer to reality => less headaches during debugging, easier maintenance of your application and you will be quicker when adding new features.
And of course, getting the total distance would be as trivial as
var totalDistance = myShip.Position.Y;

Rotating a ship 360*

In game Im trying to make, I have some ships(not space ships or so, actual ships they are in water)
If I just directly rotate them, I get absurd results.
Do I need to make 8 picture for each ship ? (considering there is 8 direction)
Are there any way that I can do it with just creating one image or at least a few, instead of 8 ?
Essentially, rotation mathematics are an interpretation of the original image.
Sure, it works depending on the complexity of the image and the relationship of straightlines and things that are perpendicular, but some things just dont work.
If you're doing a top-down 2D game with ships, I'm going to assume Sail ships here, then rotating mathematically really just isn't going to look good as the sails them selves will move and angle depending on Wind speed/direction and the angle of the ship.
Long story short ? Mathematical rotation works well for an Asteroids style triangle ship, doesn't work well for proper graphics.
Hope this helps!
If you are talking 2D graphics and are getting "absurd results" I'm assuming you're not taking into account an origin. If you have a Texture2D and give it a rotation value, it will be rotating by the default origin which is (0,0). Try setting your origin in your spritebatch.Draw call to a new Vector2(texture.width / 2, texture.height / 2) and see if that is a step in the right direction.
Another approach would be to have a spritesheet with the 8 drawings that you mention and reference a different source rectangle of the texture2D.

Detect Rotation of a scanned image in C#

We want a c# solution to correct the scanned image because it is rotated. To solve this problem we must detect the rotation angle first and then rotate the image. This was our first thought for our problem. But then we thought image warping would be more accurate as I think it would make the scanned image like our template. Then we can process it as we know all the coordinates of our template... I searched for a free SDK or a free solution in c#. Helping me in this will be great as it is the last task in our work. Really, thanks for all.
We used the PrimeOCR product to do this. It's not free, but we couldn't find a free program that was comparable.
So, the hard part is to detect the angle of the page.
If you have full control over the template, the simplest way to do this is probably to come up with an easily-detectable symbol (e.g. a solid black circle) and stick 3 of them on the template. Then, detect them (just look for big blocks of pixels with high saturation, in the case of a solid black circle).
So, you'll then have 3 sets of coordinates. If you have a top circle, a left circle, and a right circle with all 3 circles at difference distances from one another, detecting which circle is the top circle should be pretty easy.
Then just call a rotation function. This part is easy and has been done before (e.g. http://www.switchonthecode.com/tutorials/csharp-tutorial-image-editing-rotate ).
Edit:
I suggested a circle because it's easier to find the center, but a rectangle should work, too.
To be more explicit about how to actually locate the rectangles/circles, take the average Brightness value of every a × a group of pixels. If that value is greater than b, then that a × a group of pixels is part of a rectangle. a and b are varables you'll want to come up with yourself.
Use flood-fill (or, more precisely, Connected Component Labeling) group the resulting pixels together. The end result should give you your rectangles.

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