I am trying to create a scene graph for my 3D game in which every object's transformations are relative to it's parent. Each node of the graph has a Rotation, Scaling and Translation vector.
What is the correct way of combining the relative transformation matrices to get the absolute transformation of an object? I would be glad if you could also explain your solution.
Here is an example of to do it WRONG:
This actually turned out to be the solution:
Matrix GetAbsoluteTransformation()
{
if (!this.IsRoot())
{
return this.Transformation * this.Parent.GetAbsoluteTransformation();
}
else
{
return this.Transformation;
}
}
In this case, when the parent node is rotated, scaled or moved, the child is transformed the same amount, which is a correct behaviour!
But the child will only rotate around its own origin and does not move around the parent's origin.
Applications:
There is a car model with four wheels. The wheels are relative positioned around the car's origin. The wheels can rotate just like real wheels do. If I now rotate the car, the wheels should at all time stay attached to it. In this case the car is the root and the wheels are the child nodes.
Another example would be a model of the solar system. Planets rotate around their own axis, move around the sun, and moons move around planets.
With regards to your "how to do it wrong", I hate to break it to you, but it's not wrong; rather, it's incomplete. You need to do those kinds of work independently of the parent child relationship.
Here's an example of that: The wheel is attached to the car just like you mentioned. If you translate or rotate the car, you don't need to touch the wheels - they're in the same location relative to the car. However, when you try to get the wheel's new location in the 'real world', you have to traverse down the tree, applying the matrix transformations as you go. That all works, right?
When you rotate an object, it rotates around its OWN origin. So a wheel should probably be rotating around its y axis, and a planet around its z axis. But now if you need to move a planet "around the sun", you're doing something completely different. This has to be calculated separately. That's not to say it's not going to be eased by using some of the same match you already have, (although I can't say for sure without doing the math myself) but it's entirely different.
You're looking at actually changing the state of the object. That's the beauty of the scene graph! If you didn't have a scene graph, you would have to figure out all the various values all the way back to the main scene and then do all kinds of math. Here, you just have to do a little bit of trig and algebra to move around the planet (you can google the celestial mechanics) and move the planet relative to its star. The next time the main scene asks where the planet is, it will just go down the scene graph! :-D
I think this is the correct behavior.
I don't think rotating around the parent's origin is something that can be accomplished with a simple matrix stack. I think you can only propagate from parents to children.
You could try instead setting the relative rotation and transformation based on offsets from the parent's absolute origin, though that's a lot more calculations than simply pushing onto a matrix stack.
Here's a similar question: Getting absolute position and rotation from inside a scene graph?
It depends on whether you are using OpenGL or Direct3D. In OpenGL, transforms are applied right-to-left, whereas in Direct3D, they apply left-to-right. They are both perfectly valid ways of designing the transform system, but it means you have to think about them differently.
I find it easiest to think in OpenGL's system, but in reverse. Instead of thinking about how the vertices of an object move around as transforms are applied right-to-left, I imagine the coordinate system of the object being transformed in a left-to-right order. Each transform is applied relative to the new local coordinate system, not relative to the world.
In the case of the wheels on the car, there are three transforms involved: the car's position in space, a wheel's origin relative to the car, and the wheel's orientation relative to its neutral position. Simply apply these in left-to-right order (or vice-versa for Direct3D). To draw four wheels, first apply the car's transform, then remember the current transform, then apply the location and orientation transforms in turn, going back to the remembered car transform after each.
Related
for a personal project, I've created a simple 3D engine in python using as little libraries as possible. I did what I wanted - I am able to render simple polygons, and have a movable camera. However, there is a problem:
I implemented a simple flat shader, but in order for it to work, I need to know the camera location (the camera is my light source). However, the problem is that I have no way of knowing the camera's location in the world space. At any point, I am able to display my view matrix, but I am unsure about how to extract the camera's location from it, especially after I rotate the camera. Here is a screenshot of my engine with the view matrix. The camera has not been rotated yet and it is very simple to extract its location (0, 1, 4).
However, upon moving the camera to a point between the X and Z axes and pointing it upwards (and staying at the same height), the view matrix changes to this:
It is obvious now that the last column cannot be taken directly to determine the camera location (it should be something like (4,1,4) on the last picture).
I have tried a lot of math, but I can't figure out the way to determine the camera x,y,z location from the view matrix. I will appreciate any and all help in solving this, as it seems to be a simple problem, yet whose solution eludes me. Thank you.
EDIT:
I was advised to transform a vertex (0,0,0,1) by my view matrix. This, however, does not work. See the example (the vertex obviously is not located at the printed coordinates):
Just take the transform of the vector (0,0,0,1) with the modelview matrix: Which is simply the rightmost column of the modelview matrix.
EDIT: #ampersander: I wonder why you're trying to work with the camera location in the first place, if you assume the source of illumination to be located at the camera's position. In that case, just be aware, that in OpenGL there is no such thing as a camera, and in fact, what the "view" transform does, is move everything in the world around so that where you assume your camera to be ends up at the coordinate origin (0,0,0).
Or in other words: After the modelview transform, the transformed vertex position is in fact the vector from the camera to the vertex, in view space. Which means that for your assumed illumination calculation the direction toward the light source, is the negative vertex position. Take that, normalize it to unit length and stick it into the illumination term.
I am curious about the limits of three.js. The following question is asked mainly as a challenge, not because I actually need the specific knowledge/code right away.
Say you have a game/simulation world model around a sphere geometry representing a planet, like the worlds of the game Populous. The resolution of polygons and textures is sufficient to look smooth when the globe fills the view of an ordinary camera. There are animated macroscopic objects on the surface.
The challenge is to project everything from the model to a global map projection on the screen in real time. The choice of projection is yours, but it must be seamless/continuous, and it must be possible for the user to rotate it, placing any point on the planet surface in the center of the screen. (It is not an option to maintain an alternative model of the world only for visualization.)
There are no limits on the number of cameras etc. allowed, but the performance must be expected to be "realtime", say two-figured FPS or more.
I don't expect ayn proof in the form of a running application (although that would be cool), but some explanation as to how it could be done.
My own initial idea is to place a lot of cameras, in fact one for every pixel in the map projection, around the globe, within a Group object that is attached to some kind of orbit controls (with rotation only), but I expect the number of object culling operations to become a huge performance issue. I am sure there must exist more elegant (and faster) solutions. :-)
why not just use a spherical camera-model (think a 360° camera) and virtually put it in the center of the sphere? So this camera would (if it were physically possible) be wrapped all around the sphere, looking toward the center from all directions.
This camera could be implemented in shaders (instead of the regular projection-matrix) and would produce an equirectangular image of the planet-surface (or in fact any other projection you want, like spherical mercator-projection).
As far as I can tell the vertex-shader can implement any projection you want and it doesn't need to represent a camera that is physically possible. It just needs to produce consistent clip-space coordinates for all vertices. Fragment-Shaders for lighting would still need to operate on the original coordinates, normals etc. but that should be achievable. So the vertex-shader would just need compute (x,y,z) => (phi,theta,r) and go on with that.
Occlusion-culling would need to be disabled, but iirc three.js doesn't do that anyway.
I'm interested in drawing a stardome in THREE.js using either mesh points or a particle system.
I don't want the camera to be able to move any closer to any part of the stardome, since the stars are effectively at infinite distance.
I can think of a couple of ways to do this:
A very large mesh (or very large point/particle distances)
Camera and stardome have their movement exactly linked.
Is there any way to specify a mesh, point, or particle system is automaticaly rendered at infinite distance so it is always drawn behind any foreground objects?
I haven't used three.js, but my guess is no. OpenGL camera's need a "near clipping plane" and "far clipping plane", which effectively denote the minimum and maximum distance that it'll render things in. If you've played video games where you move too close to a wall and start to see through it, or see things in the distance suddenly vanish as you move away, those were probably the clipping planes at work.
The workaround is usually one of 2 ways:
1) Set the far clipping plane distance as high as it'll let you go. I don't know what data type three.js would use for this, but my guess is a 32-bit float.
2) Render it in "layers". Render all the stars first before anything else in the scene.
Option 2 is the one I usually use.
Even if you used option 1, you would still synchronize the position of the camera and skybox.
If you do not depth cull, draw the skybox first and match its position, but not rotation, to the camera.
Also disable lighting on the skybox. Instead, bake an ambience directly into its texture.
You're don't want things infinitely away, you just want them not to move with respect to the viewer and to not appear in front of things. The best way to do that is to prevent the viewer from getting closer to them which produces the illusion of the object being far away. The second thing is to modify your depth culling function so that the skybox is always considered further away than whatever you are currently drawing.
If you create a very large mesh object, you'll have to set your camera's far plane large enough to include the mesh which means you'll end up drawing things that you really do want to cull.
When several objects overlap on the same plane, they start to flicker. How do I tell the renderer to put one of the objects in front?
I tried to use .renderDepth, but it only works partly -
see example here: http://liveweave.com/ahTdFQ
Both boxes have the same size and it works as intended. I can change which of the boxes is visible by setting .renderDepth. But if one of the boxes is a bit smaller (say 40,50,50) the contacting layers are flickering and the render depth doesn't work anymore.
How to fix that issue?
When .renderDepth() doesn't work, you have to set the depths yourself.
Moving whole meshes around is indeed not really efficient.
What you are looking for are offsets bound to materials:
material.polygonOffset = true;
material.polygonOffsetFactor = -0.1;
should solve your issue. See update here: http://liveweave.com/syC0L4
Use negative factors to display and positive factors to hide.
Try for starters to reduce the far range on your camera. Try with 1000. Generally speaking, you shouldn't be having overlapping faces in your 3d scene, unless they are treated in a VERY specific way (look up the term 'decal textures'/'decals'). So basically, you have to create depth offsets, and perhaps even pre sort the objects when doing this, which all requires pretty low-level tinkering.
If the far range reduction helps, then you're experiencing a lack of precision (depending on the device). Also look up 'z fighting'
UPDATE
Don't overlap planes.
How do I tell the renderer to put one of the objects in front?
You put one object in front of the other :)
For example if you have a camera at 0,0,0 looking at an object at 0,0,10, if you want another object to be behind the first object put it at 0,0,11 it should work.
UPDATE2
What is z-buffering:
http://en.wikipedia.org/wiki/Z-buffering
http://msdn.microsoft.com/en-us/library/bb976071.aspx
Take note of "floating point in range of 0.0 - 1.0".
What is z-fighting:
http://en.wikipedia.org/wiki/Z-fighting
...have similar values in the z-buffer. It is particularly prevalent with
coplanar polygons, where two faces occupy essentially the same space,
with neither in front. Affected pixels are rendered with fragments
from one polygon or the other arbitrarily, in a manner determined by
the precision of the z-buffer.
"The renderer cannot reposition anything."
I think that this is completely untrue. The renderer can reposition everything, and probably does if it's not shadertoy, or some video filter or something. Every time you move your camera the renderer repositions everything (the camera is actually the only thing that DOES NOT MOVE).
It seems that you are missing some crucial concepts here, i'd start with this:
http://www.opengl-tutorial.org/beginners-tutorials/tutorial-3-matrices/
About the depth offset mentioned:
How this would work, say you want to draw a decal on a surface. You can 'draw' another mesh on this surface - by say, projecting a quad onto it. You want to draw a bullet hole over a concrete wall and end up with two coplanar surfaces - the wall, the bullet hole. You can figure out the depth buffer precision, find the smallest value, and then move the bullet hole mesh by that value towards the camera. The object does not get scaled (you're doing this in NDC which you can visualize as a cube and moving planes back and forth in the smallest possible increment), but does translate in depth direction, ending up in front of the other.
I don't see any flicker. The cube movement in 3D seems to be super-smooth. Can you try in a different computer (may be faster one)? I used Chrome on Macbook Pro.
I'd like to implement a dragging feature where users can drag objects around the workspace. That of course is the easy bit. The hard bit is to try and make it a physically correct drag which incorporates rotation due to torque moments (imagine dragging a book around on a table using only one finger, how does it rotate as you drag?).
Does anyone know where I can find explanations on how to code this (2D only, rectangles only, no friction required)?
Much obliged,
David
EDIT:
I wrote a small app (with clearly erroneous behaviour) that I hope will convey what I'm looking for much better than words could. C# (VS 2008) source and compiled exe here
EDIT 2:
Adjusted the example project to give acceptable behaviour. New source (and compiled exe) is available here. Written in C# 2008. I provide this code free of any copyright, feel free to use/modify/whatever. No need to inform me or mention me.
Torque is just the applied force projected perpendicular to a vector between the point where the force is applied and the centroid of the object. So, if you pull perpendicular to the diameter, the torque is equal to the applied force. If you pull directly away from the centroid, the torque is zero.
You'd typically want to do this by modeling a spring connecting the original mouse-down point to the current position of the mouse (in object-local coordinates). Using a spring and some friction smooths out the motions of the mouse a bit.
I've heard good things about Chipmunk as a 2D physics package:
http://code.google.com/p/chipmunk-physics/
Okay, It's getting late, and I need to sleep. But here are some starting points. You can either do all the calculations in one coordinate space, or you can define a coordinate space per object. In most animation systems, people use coordinate spaces per object, and use transformation matrices to convert, because it makes the math easier.
The basic sequence of calculations is:
On mouse-down, you do your hit-test,
and store the coordinates of the
event (in the object coordinate
space).
When the mouse moves, you create a
vector representing the distance
moved.
The force exterted by the spring is k * M, where M is the amount of distance between that initial mouse-down point from step 1, and the current mouse position. k is the spring constant of the spring.
Project that vector onto two direction vectors, starting from the initial mouse-down point. One direction is towards the center of the object, the other is 90 degrees from that.
The force projected towards the center of the object will move it towards the mouse cursor, and the other force is the torque around the axis. How much the object accelerates is dependent on its mass, and the rotational acceleration is dependent on angular momentum.
The friction and viscosity of the medium the object is moving in causes drag, which simply reduces the motion of the object over time.
Or, maybe you just want to fake it. In that case, just store the (x,y) location of the rectangle, and its current rotation, phi. Then, do this:
Capture the mouse-down location in world coordinates
When the mouse moves, move the box according to the change in mouse position
Calculate the angle between the mouse and the center of the object (atan2 is useful here), and between the center of the object and the initial mouse-down point. Add the difference between the two angles to the rotation of the rectangle.
This would seem to be a basic physics problem.
You would need to know where the click, and that will tell you if they are pushing or pulling, so, though you are doing this in 2D, your calculations will need to be in 3D, and your awareness of where they clicked will be in 3D.
Each item will have properties, such as mass, and perhaps information for air resistance, since the air will help to provide the motion.
You will also need to react differently based on how fast the user is moving the mouse.
So, they may be able to move the 2 ton weight faster than is possible, and you will just need to adapt to that, as the user will not be happy if the object being dragged is slower than the mouse pointer.
Which language?
Here's a bunch of 2d transforms in C