I'm experimenting with LibGDX and 3D in a projection view. Right now I'm looking at how to determine the outermost bounds of my viewport in world space at z=0.0, in order to draw coordinate grid no larger than necessary. However, I seem to have outpaced my education in that I haven't taken a formal linear algebra class and am still a little fuzzy on matrix math.
Is there a way to determine where I should start and stop drawing lines without resorting to using picking and drawing a transparent plane to intersect with?
LibGDX's unproject function takes screen coordinates in a Vector3 and returns a Vector3 in world space from the near clipping plane to the far, given the provided z. However, given that I have a translated and rotated Camera (an encapsulation of the viewprojection matrix and a slew of convenience methods), it occurs to me that I can't pick an arbitrary z to put in the window coordinate vector and just set it to 0.0 after unprojection, as that point probably won't be the furthest viewable point in the viewport. So how do I know what z value to use in the window coordinate that will give the the x and y I need in world space that's at z=0.0?
EDIT (UPDATE):
So apparently it looks like the problem I'm looking at is plane intersection, which would require ray tracing. So now I suppose my question is this: is ray tracing 4 times per render loop (or, I suppose whenever the camera has moved) worth the payoff of being able to dynamically draw a worldspace coordinate grid no larger than the viewport? If not, is there a cheaper algorithm I can use to estimate where I should start and stop drawing lines?
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Over the past few weeks I've been attempting to learn the libGDX library. I'm finding it hard, especially for my first endeavor toward game development, to comprehend the system of Camera/viewport relationships. One line of code that I've been told to use, and the API mentions, is:
batch.setProjectionMatrix(camera.combined);
Despite a good 4 hours of research, I'm still lacking a complete understanding of the functionality of this code. It is to my basic understanding that it "tells" the batch where the camera is looking. My lack of comprehension is depressing and angering, and I'd appreciate if anyone could assist me. Another issue with the code snippet is that I'm unsure of when it's necessary to implement (in the render method, create method, etc).
Consider taking a picture with a camera. E.g. using your smartphone camera taking a picture of a bench in the park. When you do that, then you'll see the bench in the park on the screen of your smartphone. This might seem very obvious, but let's look at what this involves.
The location of the bench on the picture is relative to where you were standing when taking the photo. In other words, it is relative to the camera. In a typical game, you don't place object relative to the object. Instead you place them in your game world. Translating between your game world and your camera, is done using a matrix (which is simply a mathematical way to transform coordinates). E.g. when you move the camera to the right, then the bench moves to the left on the photo. This is called the View matrix.
The exact location of the bench on the picture also depends on the distance between bench and the camera. At least, it does in 3D (2D is very similar, so keep reading). When it is further away it is smaller, when it is close to the camera it is bigger. This is called a perspective projection. You could also have an orthographic projection, in which case the size of the object does not change according to the distance to the camera. Either way, the location and size of the bench in the park is translated to the location and size in pixels on the screen. E.g. the bench is two meters wide in the park, while it is 380 pixels on the photo. This is called the projection matrix.
camera.combined represents the combined view and projection matrix. In other words: it describes where things in your game world should be rendered onto the screen.
Calling batch.setProjectionMatrix(cam.combined); instruct the batch to use that combined matrix. You should call that whenever the value changes. This is typically when resize is called and also whenever you move or otherwise alter the camera.
If you are uncertain then you can call that in the start of your render method.
The other answer is excellent, but I figure a different way of describing it might help it to click.
You generally deal with your game in "world space", a coordinate system that is analogous to the real world. In linear algebra, you can convert points in space from one coordinate system to another by multiplying the point's coordinates by a matrix that represents the relation between two coordinate systems.
The view matrix is multiplied by a point to convert it from world space to camera space (the camera's point of view). The projection matrix is used to convert a point from camera space to screen space (the flat 2D rectangle of your device's screen). When you call update() on a camera in Libgdx, it applies your latest changes to position, orientation, viewport size, field of view, etc. to its view and projection matrices so they can be used in shaders.
You rarely need to deal with stuff in camera space in 2D, so SpriteBatch doesn't need separate view and projection matrices. They can be combined into a single matrix that converts straight from world space to screen space, which is already done automatically in the Camera, hence the camera.combined matrix.
SpriteBatch has a default built-in shader that multiplies this projection matrix by all the vertices of your sprites so they will be properly mapped to the flat screen.
You should call setProjectionMatrix whenever you have moved the camera or resized the screen.
There is a third type of matrix called a model matrix that is used for 3D stuff. A model matrix describes the model's orientation, scale, and position in world space. So it is multiplied by coordinates in the model to move them from local space to world space.
Take for example a basic sidescrolling game. As the player moves to the side, the camera pans to follow them. This means that where objects are in the world doesn't necessarily correspond to where they are on the screen, since the screen and the world move relative to each other.
Here's an example: say your screen is 100px*100px square (for some reason). You place an object at position (50, 0), so it's now in the middle and at the bottom of the screen. Now say you move your player over to the right, and the whole screen pans to follow the player. This means that the object you placed earlier should have moved left on the screen. So it's still at (50, 0) in the world, since it didn't actually move relative to the rest of the scenery, but it should now be drawn at, say, (10, 0) on the screen, since which part of the world the screen is looking at has changed. This is the difference between "worldspace" (where an object is in the world) and "screenspace" (where the object is drawn on the actual display).
When you try to draw with a SpriteBatch, it is by default going to assume worldspace coordinates are the same as screenspace coordinates: when you say "draw at (50, 0)", it's going to draw the object at (50, 0) on the screen. Even if the camera moves, it's always going to draw at (50, 0) on the screen, so as the camera pans, the object will follow and stay stuck to the same place on the screen.
Since you usually don't want that, you give the SpriteBatch a projection matrix, which is a transformation matrix that tells how to convert screenspace coordinates to worldspace coordinates, and vice versa. This way, when you tell the batch "draw at (50, 0)", it can look at the matrix it got from the camera and see that, since the camera has moved, (50, 0) in the world actually means (10, 0) on the screen, and it will draw your sprite in the right place.
Let's say I have a triangular face in 3d space, and I have the 3d coordinates of each vertex of this triangle, and would also have other information about the triangle(angles, lengths of sides, etc.). In Java, if I have the viewing screen and its information, how can I draw that plane, without using libraries like LWJGL, to that image, assuming I can properly project, accounting for perspective, any 3d point to that 2d image.
Would the best course of action just be to run a loop that draws each point on the plain to a point on the image(i.e. setting the corresponding pixel), which will most likely set the same pixel multiple times? If I'd do this, what would be the best way to identify each point in an oblique triangle, or a triangle that doesn't line up nicely with the axes?
tl;dr: I have a triangular face in 3d space, a "camera" looking at the face, and an image in which I can set each pixel. Using no GL libraries, what's the best way to project and draw that face onto the image?
Projection :
won't detail as you seems to know it
Drawing a line
you can look at Bresenham algorithm if you wanna start with the basics
(hardwared in recent graphics card)
Filling
you can fill between left and right borders of the triangle while you use Bresenham on both (you could use a floodfill algorithm starting ... i don't know, maybe at the projection of the center of the triangle)
Your best bet is to check out the g.fillPolygon() function for Java. It allows you to draw polygons with as many sides as possible and theres also g.drawPolygon() if you don't want it solid. Then you can just do some simple maths for the points. Such as each point is basically it's x and y except if the polygon is further away the points move closer to the center of the polygon and if the polygon is closer they move further away from the center of the polygon.
A second idea could be using some sort of array to store pixels and then researching line drawing algorithms and drawing lines then putting all the line data in another array and using some sort of flood-fill. Then whilst it's in that array you could try and do some weird stuff to the pixels if you wanted textures or something.
I know do a horizontal and vertical scroller game (like Mario), in this game type, the character is always in the same distance from user. The character only moves to left and right in horizontal scroller and to down and up in vertical scroller.
But there are games in 2D that the character can move freely in the scene, like for example graphic adventures.
So how can I do that ground in order to move the character freely on the ground with depth sense?
An example can see in this video: http://youtu.be/DbZZVbF8fZY?t=4m17s
Thanks you.
This is how I would do that:
First imagine that you are looking at your scene from the top to the ground. Set your coordinate system like that. So all object on your scene will have X and Y coordinates. All your object movements and checking (when character bumps into a wall or something), calculations do in that 2D world.
Now, to draw your world, if you want simpler thing, without some isometric perspective 3D look you just to draw your background image first, and then order all your objects far to near and draw them that way. Devide your Y coords to squeeze movement area a bit. Add some constant to Y to move that area down. If you characters can jump or fly (move trough Y axe) just move Y coord to for some amount.
But if you want it to be more 3D you'll have to make some kind of perspective transformation - multiply your X coordinate with Y and some constant (start with value 1 for constant and tune it up until optimal value). You can do similar thing with Y coord too, but don't think it's needed for adventure games like this.
This is probably hard to understand without the image, but it's actually very simple transformation.
While working on Projectiles I thought that it would be a good idea to rotate the sprite as well, to make it look nicer.
I am currently using a 1-Dimensional Array, and the sprite's width and height can and will vary, so it makes it a bit more difficult for me to figure out on how to do this correctly.
I will be honest and straight out say it: I have absolutely no idea on how to do this. There have been a few searches that I have done to try to find some stuff, and there were some things out there, but the best I found was this:
DreamInCode ~ Rotating a 1-dimensional Array of Pixels
This method works fine, but only for square Sprites. I would also like to apply this for non-square (rectangular) Sprites. How could I set it up so that rectangular sprites can be rotated?
Currently, I'm attempting to make a laser, and it would look much better if it didn't only go along a vertical or horizontal axis.
You need to recalculate the coordinate points of your image (take a look here). You've to do a matrix product of every point of your sprite (x, y) for the rotation matrix, to get the new point in the space x' and y'.
You can assume that the bottom left (or the bottom up, depends on your system coordinate orientation) of your sprite is at (x,y) = (0,0)
And you should recalculate the color too (because if you have a pure red pixel surrounded by blue pixel at (x,y)=(10,5) when you rotate it can move for example to (x, y)=(8.33, 7.1) that it's not a real pixel position because pixel haven't float coordinate. So the pixel at real position (x, y)=(8, 7) will be not anymore pure red, but a red with a small percentage of blue)... but one thing for time.
It's easier than you think: you only have to copy the original rectangular sprites centered into bigger square ones with transparent background. .png files have that option and I think you may use them.
I'm working on making a 2D isometric engine in Java because I like suffering, I guess. Anyways, I'm getting into collision detection and I've hit a bit of a problem.
Characters in-game are not restricted to movement from tile to tile - they move freely. My problem is that I'm not sure how to stop a player from colliding with, say, a crate, without denying them access to the tile.
For instance, say the crate was on .5 of a tile, and then the rest of the crate was off the tile, I'd like the player to be able to move on to the free .5 of the tile instead of the entire tile becoming blocked.
The problem I've hit is that I'm not sure how to approximate the size of the footprint of the object. Using the image's dimensions don't work very well, since the object's "height" in gamespace translates to additional floorspace being taken up by the image.
How should I estimate an object's size? Mind, I don't need pixel-perfect detection. A rhombus would work fine.
I'm happy to provide any code you might need, but this seems like a math issue.
From the bounding rectangle of the sprite, you can infer the height of a rhombus that fits inside, but you cannot precisely determine the two dimensions on the floor, as each dimension contributes equally to width and height of the sprite. However, if you assume that the base of the rhombus square then you can determine the length of its side as well.
If the sprite is W pixels wide and H pixels high, the square base of the rhombus has a side of W / sqrt(3) and the height of the rhombus will be H - (W / sqrt(3)). This image of some shapes in isometric projection can be helpful to understand why these formulas work.