I am trying to create an application similar in UI to Sketchup. As a first step, I need to display the ground surface stretching out in all directions. What is the best way to do this?
Options:
Create a sufficiently large regular polygon stretching out in all directions from the origin. Here there is a possibility of the user hitting the edges and falling off the surface of the earth.
Model the surface of the earth as a sphere/spheroid. Here I will be limiting my vertex co-ordinates to very large values prone to rounding off errors. (Radius of earth is 6371000000 millimeter).
Same as 1 but dynamically extend the ends of the earth as the user gets close to them.
What is the usual practice?
I guess you would do neither of these, but instead use a virtual ground.
So you just find out, what portion of the ground is visible in the viewport and then create a plane large enough to fill that. With some reasonable maxiumum, which simulates the end of the line of sight aka horizon as we know it.
Related
In computer graphics, why do we need to know that backward face and forward face of a polygon are different?
There are several reasons why a triangle's face might be important.
Face Culling
If you draw a cube, you can only ever see at most 3 sides of it. The front three sides will block your view of the back 3 sides. And while depth testing will prevent drawing the fragments corresponding to the back sides... why bother? In order to do depth testing, you have to rasterize those triangles. That's a lot of work for triangles that won't be seen.
Therefore, we have a way to cull triangles based on their facing, before performing rasterization on them. While vertex processing will still be done on those triangles, they will be discarded before doing heavy-weight operations like rasterization.
Through face culling, you can eliminate approximately half of the triangles in a closed mesh. That's a pretty decent performance savings.
Two-Sided Rendering
A leaf is a thin object, so you might render it as one flat polygon, without face culling. However, a leaf does not look the same on both sides. The top side is usually quite a bit darker than the bottom side.
You can achieve this effect by sending two colors when rendering the leaf; one meant for the top side and one for the bottom. In your fragment shader, you can detect which side of the polygon that fragment was generated from, by looking at the built-in variable gl_FrontFacing. That boolean can be used to select which color to use.
It could even be used to select which texture to sample from, if you want to do more complex two-sided rendering.
I'm building a 2D game where player can only see things that are not blocked by other objects. Consider this example on how it looks now:
I've implemented raytracing algorithm for this and it seems to work just fine (I've reduced the boundaries for demo to make all edges visible).
As you can see, lighter area is built with a bunch of triangles, each of them having common point in the position of player. Each two neighbours have two common points.
However I'm willing to calculate bounds for external the part of the polygon to fill it with black-colored triangles "hiding" what player cannot see.
One way to do it is to "mask" the black rectangle with current polygon, but I'm afraid it's very ineffective.
Any ideas about an effective algorithm to achieve this?
Thanks!
A non-analytical, rough solution.
Cast rays with gradually increasing polar angle
Record when a ray first hits an object (and the point where it hits)
Keep going until it no longer hits the same object (and record where it previously hits)
Using the two recorded points, construct a trapezoid that extends to infinity (or wherever)
Caveats:
Doesn't work too well with concavities - need to include all points in-between as well. May need Delaunay triangulation etc... messy!
May need extra states to account for objects tucked in behind each other.
I am looking for an algorithm that given two meshes could clip one using another.
The simplest form of this is clipping a mesh using a plane. I've already implemented that by following something similar to what is described here.
What it does is basically inspecting all mesh vertices and triangles with respect to the plane (the plane's normal and point are given). If the triangle is completely above the plane, it is left untouched. If it falls completely below the plane, it is discarded. If some of the edges of the triangle intersect with the plane, the intersecting points with the plane are calculated and added as the new vertices. Finally a cap is generated for the hole on the place the mesh was cut.
The problem is that the algorithm assumes that the plane is unlimited, therefore whatever is in its path is clipped. In the simplest form, I need an extension of this without the assumption of a plane of "infinite" size.
To clarify, imagine that we have a 3D model of a desk with 2 boxes on it. The boxes are adjacent (but not touching or stacked). The user will define a cutting plane of a limited width and height underneath the first box and performs the cut. We end up with a desk model (mesh) with a box on it and another box (mesh) that can be freely moved around/manipulated.
In the general form, I'd like the user to be able to define a bounding box for the box he/she wants to separate from the desk model and perform the cut using that bounding box.
If I could extend the algorithm I already have to an algorithm with limited-sized planes, that would be great for now.
What you're looking for are constructive solid geometry/boolean algorithms with arbitrary meshes. It's considerably more complex than slicing meshes by an infinite plane.
Among the earliest and simplest research in this area, and a good starting point, is Constructive Solid Geometry for Polyhedral Objects by Trumbore and Hughes.
http://cs.brown.edu/~jfh/papers/Laidlaw-CSG-1986/main.htm
From the original paper:
More elaborate solutions extend upon this subject with a variety of data structures.
The real complexity of the operation lies in the slicing algorithm to slice one triangle against another. The nightmare of implementing robust CSG lies in numerical precision. It's easy when you involve objects far more complex than a cube to run into cases where a slice is made just barely next to a vertex (at which point you have the tough decision of merging the new split vertex or not prior to carrying out more splits), where polygons are coplanar (or almost), etc.
So I suggest initially erring on the side of using very high-precision floating point numbers, possibly even higher than double precision to focus on getting something working correctly and robustly. You can optimize later (first pass should be to use an accelerator like an octree/kd-tree/bvh), but you'll avoid many headaches this way in your first iteration.
This is vastly simpler to implement at render time if you're focusing on a raytracer rather than a modeling software, e.g. With raytracers, all you have to do to do this kind of arbitrary clipping is pretend that an object used to subtract from another has its polygons flipped in the culling process, e.g. It's easy to solve robustly at the ray level, but quite a bit harder to do robustly at the geometric level.
Another thing you can do to make your life so much easier if you can afford it is to voxelize your object, find subtractions/additions/unions of voxels, and then translate the voxels back into a mesh. This is so much easier to make robust, but harder to do efficiently and the voxel->polygon conversion can get quite involved if you want better results than what marching cubes provide.
It's a really tough area to do extremely well and requires perseverance, and thus the reason for the existence of things like this: http://carve-csg.com/about.
If someone is interested, currently there is a solution for this problem in CGAL library. It allows clipping one triangular mesh using another mesh as bounding volume. The usage example can be found here.
I am using Java to write a very primitive 3D graphics engine based on The Black Art of 3D Game Programming from 1995. I have gotten to the point where I can draw single color polygons to the screen and move the camera around the "scene". I even have a Z buffer that handles translucent objects properly by sorting those pixels by Z, as long as I don't show too many translucent pixels at once. I am at the point where I want to add lighting. I want to keep it simple, and ambient light seems simple enough, directional light should be fairly simple too. But I really want point lighting with the ability to move the light source around and cast very primitive shadows ( mostly I don't want light shining through walls ).
My problem is that I don't know the best way to approach this. I imagine a point light source casting rays at regular angles, and if these rays intersect a polygon it will light that polygon and stop moving forward. However when I think about a scene with multiple light sources and multiple polygons with all those rays I imagine it will get very slow. I also don't know how to handle a case where a polygon is far enough away from a light source that if falls in between two rays. I would give each light source a maximum distance, and if I gave it enough rays, then there should be no point within that distance that any two rays are too far apart to miss a polygon, but that only increases my problem with the number of calculations to perform.
My question to you is: Is there some trick to point light sources to speed them up or just to organize it better? I'm afraid I'll just get a nightmare of nested for loops. I can't use openGL or Direct3D or any other cheats because I want to write my own.
If you want to see my results so far, here is a youtube video. I have already fixed the bad camera rotation. http://www.youtube.com/watch?v=_XYj113Le58&feature=plcp
Lighting for real time 3d applications is (or rather - has in the past generally been) done by very simple approximations - see http://en.wikipedia.org/wiki/Shading. Shadows are expensive - and have generally in rasterizing 3d engines been accomplished via shadow maps & Shadow Volumes. Point lights make shadows even more expensive.
Dynamic real time light sources have only recently become a common feature in games - simply because they place such a heavy burden on the rendering system. And these games leverage dedicated graphics cards. So I think you may struggle to get good performance out of your engine if you decide to include dynamic - shadow casting - point lights.
Today it is commonplace for lighting to be applied in two ways:
Traditionally this has been "forward rendering". In this method, for every vertex (if you are doing the lighting per vertex) or fragment (if you are doing it per-pixel) you would calculate the contribution of each light source.
More recently, "deferred" lighting has become popular, wherein the geometry and extra data like normals & colour info are all rendered to intermediate buffers - which is then used to calculate lighting contributions. This way, the lighting calculations are not dependent on the geometry count. It does however, have a lot of other overhead.
There are a lot of options. Implementing anything much more complex than some the basic models that have been used by dedicated graphics cards over the past couple of years is going to be challenging, however!
My suggestion would be to start out with something simple - basic lighting without shadows. From there you can extend and optimize.
What are you doing the ray-triangle intersection test for? Are you trying to light only triangles which the light would reach? Ray-triangle
intersections for every light with every poly is going to be very expensive I think. For lighting without shadows, typically you would
just iterate through every face (or if you are doing it per vertex, through every vertex) and calculate & add the lighting contribution per light - you would do this just before you start rasterizing as you have to pass through all polys in anycase.
You can calculate the lighting by making use of any illumination model, something very simple like Lambertian reflectance - which shades the surface based upon the dot product of the normal of the surface and the direction vector from the surface to the light. Make sure your vectors are in the same spaces! This is possibly why you are getting the strange results that you are. If your surface normal is in world space, be sure to calculate the world space light vector. There are a bunch of advantages for calulating lighting in certain spaces, you can have a look at that later on, for now I suggest you just get the basics up and running. Also have a look at Blinn-phong - this is the shading model graphics cards used for many years.
For lighting with shadows - look into the links I posted. They were developed because realistic lighting is so expensive to calculate.
By the way, LaMothe had a follow up book called Tricks of the 3D Game Programming Gurus-Advanced 3D Graphics and Rasterization.
This takes you through every step of programming a 3d engine. I am not sure what the black art book covers.
From the oldest games to the very modern, it seems like you can still see through walls or most often the ground in some camera positions.
Why is collision difficult to effectively compute in graphics engines?
Is it rounding/loss of precision accumulating leading to a mis-rendered view?
This is not actually collision in the explicit sense. The camera position is probably not actually "inside" the wall or the ground in those situations, but it is simply very close to it.
In computer 3D graphics the camera has a concept of a near plane and a far plane. Only geometry located between these two planes will be visible, while the rest will be clipped. If you are too close to something and align the camera correctly, then chances are that some parts of the geometry will be too close to the camera as defined by the near plane and as a result that geometry will not be rendered.
Now, the distance to this near plane can be set by the developers, and it can be set to be very short - short enough to ensure that situations like these cannot occur. However, the depth buffer or z buffer that is used to determine which objects are closest to the camera during rendering, and thus which objects to render and which not to render, is closely related to the near and far plane distances.
In graphics hardware the depth buffer is represented using a fixed amount of bits for each pixel, for example 32 bits. These 32 bits must be enough to accurately represent the entire span between the near plane and the far plane. It is also not linear, but will use more precision closer to the camera. As a result, choosing a very small near plane distance will greatly reduce the overall precision of the depth buffer. This can cause annoying flickering throughout the entire scene wherever two objects are very close to each others.
You can read more about this issue here as well as section 12.040 here.
It's not about difficulty (of course, it's not easy to compute collision/clipping of non-convex object), but you still have only like ~33ms to compute whole frame, so some compromise have to be made (collision mesh is not the same like mesh you really see). If there is no time for precise solution (to fulfill all conditions - camera distance, object which have to be seen, collision avoidance), you have to fallback to some "easy" solution like see through the wall.