What the minimum configuration for the program I need to build 3D Graphics from scratch, for example I have only SFML for working with 2d graphics and I need to implement the Camera object that can move & rotate in a space
Where to start and how to implement vector3d -> vector2d conversion functions and other neccessary things
All I have for now is:
angles Phi, Xi, epsilon 1-3 and some object that I can draw on the screen with the following formula
x/y = center.x/y + scale.x/y * dot(point[i], epsilon1/epsilon2)
But this way Im just transforming "world" axis, not the Object points
First you need to implement transform matrix and vector math:
Mathematically compute a simple graphics pipeline
Understanding 4x4 homogenous transform matrices
The rest depends on kind of rendering you want to achieve:
boundary polygonal mesh rendering
This kind of rendering is the native for nowadays gfx cards. You need to implement buffers for:
depth (for filled polygons without z-sorting)
screen (to avoid flickering and also serves as Canvas)
shadow,stencil,aux (for advanced rendering techniques)
they have usually the same resolution as target rendering area. On top of this you need to implement supported primitives rendering at least point,line,triangle. see:
Algorithm to fill triangle
on top of all this you can add textures,shaders and whatever else you want to ...
(back)ray tracing
this kind of rendering is very different and current gfx HW is not build for it. This involves implementing ray/primitives intersections computation, Snell's law and analytical representation of meshes. This way you can also do multi-spectral rendering and more physically accurate effects/processes see:
How can I render an 'atmosphere' over a rendering of the Earth in Three.js? hybrid approach #1+#2
Algorithm for 2D Raytracer
How to implement 2D raycasting light effect in GLSL
Multi-Band Image raster to RGB
The difference between 2D and 3D ray tracer is almost none the only difference is how to compute perpendicular vector ...
There are also different rendering methods like Volume rendering, hybrid methods and others but their implementation is usually task oriented and generic description would most likely just mislead ... Here some 3D ray tracers of mine:
back raytrace through 3D mesh
back raytrace through 3D volume
Related
Plotting packages offer a variety of methods for displaying data. Write an interactive plotting application for two dimensionsional curves. Your application should be able to allow the user to choose the mode (line strip or polyline display of the data, bar chart or pie charts), colours, and line styles.
You should start with the GUI editation like this:
Does anyone know of a low level (no frameworks) example of a drag & drop, re-order-able list?
and change it to your primitives (more points per primitive instead of one ... handle each point as (sub)object so you can change its position later).
Then just add tools like add object,del object,... For hand drawing tool use piece wise interpolation cubics
The grid can be done like this:
How to draw dynamic 2D grid that adjusts according to camera zoom: OpenGL
Mouse zooming/panning is also important
Zooming graphics based on current mouse position
Putting all above together into simple editor looks like this:
Using GPU for curve rendering might give you some nice speed and functionality boost:
Is it possible to express "t" variable from Cubic Bezier Curve equation?
Mouse selection of objects might be a speed problem if your scene contains too many objects so in such case its best to use index buffers where you can mouse select with pixel perfect precision for almost free in O(1):
OpenGL 3D-raypicking with high poly meshes
The example is for 3D , in 2D is much simpler ...
Also do not forget to implement save/load functionality to some vector file format. I recommend using SVG it might be complicated to start with it but you can quickly check it contents in any SVG viewer or browser also in notepad as its just a text file. If you use just basic path elements and ignore the rest of SVG features you will see the parsing and creating SVG is not that hard for example See these:
Get Vertices/Edges From BMP or SVG (C#)
Discrete probability distribution plot with given values
For really big datasets you might want to use spatial subdivision techniques (Bounding (Volume)Area Hierarchy, or Quad tree) to ease up the operations...
More in depth implementation details about 2D vector gfx editors depends on language, OS, gfx api and GUI api you using and task you are aiming for ...
This is a question to understand the principles of GPU accelerated rendering of 2d vector graphics.
With Skia or Direct2D, you can draw e.g. rounded rectangles, Bezier curves, polygons, and also have some effects like blur.
Skia / Direct2D offer CPU and GPU based rendering.
For the CPU rendering, I can imagine more or less how e.g. a rounded rectangle is rendered. I have already seen a lot of different line rendering algorithms.
But for GPU, I don't have much of a clue.
Are rounded rectangles composed of triangles?
Are rounded rectangles drawn entirely by wild pixel shaders?
Are there some basic examples which could show me the basic prinicples of how such things work?
(Probably, the solution could also be found in the source code of Skia, but I fear that it would be so complex / generic that a noob like me would not understand anything.)
In case of direct2d, there is no source code, but since it uses d3d10/11 under the hood, it's easy enough to see what it does behind the scenes with Renderdoc.
Basically d2d tends to have a policy to minimize draw calls by trying to fit any geometry type into a single buffer, versus skia which has some dedicated shader sets depending on the shape type.
So for example, if you draw a bezier path, Skia will try to use tesselation shader if possible (which will need a new draw call if the previous element you were rendering was a rectangle), since you change pipeline state.
D2D, on the other side, tends to tesselate on the cpu, and push to some vertexbuffer, and switches draw call only if you change brush type (if you change from one solid color brush to another it can keep the same shaders, so it doesn't switch), or when the buffer is full, or if you switch from shape to text (since it then needs to send texture atlases).
Please note that when tessellating bezier path D2D does a very great work at making the resulting geometry non self intersecting (so alpha blending works properly even on some complex self intersecting path).
In case on rounded rectangle, it does the same, just tessellates into triangles.
This allows it to minimize draw calls to a good extent, as well as allowing anti alias on a non msaa surface (this is done at mesh level, with some small triangles with alpha). The downside of it is that it doesn't use much hardware feature, and geometry emitted can be quite high, even for seemingly simple shapes).
Since d2d prefers to use triangle strips instead or triangle list, it can do some really funny things when drawing a simple list of triangles.
For text, d2d use instancing and draws one instanced quad per character, it is also good at batching those, so if you call some draw text functions several times in a row, it will try to merge this into a single call as well.
There are some 3D applications which can cast shadow or silhouette below 3D models. They render pretty fast and smooth. I wonder what kind of technology is the standard procedure to get 3D model shadow/silhouette.
For example is there any C++ library like libigl or CGAL to get shadow/silhouette pretty fast? Or maybe GLSL shading is used? Any hint would be appreciated on the standard technology stack.
For rendering, it's trivial. Just project the vertices to the surface (for the case of the XY plane, this just entails setting the Z coordinate to 0) and render the triangles. There'll be a lot of overlap, but since you're just rendering that won't matter.
If you're trying to build a set of polygons representing the silhouette shape, you'll need to instead union the projected triangles using something like the Vatti clipping algorithm.
Computing shadows is a vast and uneasy topic. In the real world, light sources are extended and the shadow edges are not sharp (there is penumbra). Then there are cast shadows, and even self-shadows.
If you limit yourself to punctual light sources (hence sharp shadows), there is a simple principle: if you place an observer at the light source, the faces he will see are illuminated by that light source. Conversely, the hidden surfaces are in the shadow.
For correct rendering, the shadowed areas should be back-projected to the scene and painted black.
By nature, the ray-tracing techniques make this process easy to implement.
I know that there are 4 techniques to draw 3D objects:
(1) Wireframe Modeling and rendering, (2) Additive Modeling, (3) Subtractive Modeling, (4) Splines and curves.
Then, those models go through hidden surface removal algorithm.
Am I correct?
Be that way, What formula or algorithm can I use to draw a 3D Sphere?
I am using a low-level library named WinBGIm from colorado university.
there are 4 techniques to draw 3D objects:
(1) Wireframe Modeling and rendering, (2) Additive Modeling, (3) Subtractive Modeling, (4) Splines and curves.
These are modelling techniques and not rendering techniques. They allow you to mathematically define your mesh's geometry. How you render this data on to a 2D canvas is another story.
There are two fundamental approaches to rendering 3D models on a 2D canvas.
Ray Tracing
The basic idea of ray tracing is to pass a ray from the camera's origin, through the point on the canvas whose colour needs to be determined. Determine which models get hit by it and pick the closest one, determine how it's lit to compute the colour there. This is done by further tracing rays from the hit point to all the light sources in the scene. If you notice, this approach eliminates the need to use hidden surface determination algorithms like the back face culling, z-buffer, etc. since the basic idea is rooted on a hidden surface algorithm (ray tracing).
There are packages, libraries, etc. that help you do this. However, it's common that ray tracers are written from scratch as a college-level project. However, this approach takes more time to render (not to code), but the results are generally more pleasing than the below one. This approach is more popular when you want to render non-interactive visuals like movies.
Rasterization
This approach takes primitives (triangles and quads) that define the models in the scene and sample them at regular intervals (screen pixels they cover) and write it on to a colour buffer. Here hidden surface is usually eliminated using the Z-buffer; a buffer that stores the z-order of the fragment and the closer one wins, when writing to the colour buffer.
Rasterization is the more popular approach with cheap hardware support for it available on most modern computers due to years of research and money that has gone in to it. Libraries like OpenGL and Direct3D are readily available to facilitate development. Although the results are less pleasing than ray tracing, it's faster to render and thus is widely used in interactive, real-time rendering like games.
If you want to not use those libraries, then you have to do what is commonly known as software rendering i.e. you will end up doing what these libraries do.
What formula or algorithm can I use to draw a 3D Sphere?
Depends on which one of the above you choose. If you simply rasterize a 3D sphere in 2D with orthographic projection, all you have to do is draw a circle on the canvas.
If you are looking for hidden lines removal (drawing the edges rather than the inside of the faces), the solution is easy: "back face culling".
Every edge of your model belongs to two faces. For every face you can compute the normal vector and check if it is facing to the observer (by the sign of the dot product of the normal and the direction of the projection line); in other words, if the observer is located in the outer half-space defined by the plane of the face. Then an edge is wholly visible if and only if it belongs to at least one front face.
Usual discretization of the sphere are made by drawing equidistant parallels and meridians. It may be advantageous to adjust the spacing of the parallels so that all tiles are about the same area.
I am trying to create a 3-dimensional game that is based entirely off of cubes of the exact same size. I wanted to learn how to make my own 3-dimensional game using only 2-dimensional game libraries. Currently, the way I am doing is that I have an array storing the locations of all the centers of each cube in the game. Then, when drawing a single cube, I figure out which 3 sides of the cube I need to draw (since you don't need to draw all 3 sides of the cube). Then, knowing the 3-dimensional points of all the corners of the cube, I project those points onto a 2 dimensional space using the camera position, camera angle, and the point I am projecting.
Now my real question is: Now that I can draw a single cube, how do I draw multiple cubes, considering that cubes need to be drawn in a certain order (i.e. the cubes that are further away need to be drawn first so that the cubes that are closer to us appear on top of the cubes far away from us)? How do I determine which cubes to draw first given the list of cube centers and their sizes, and the camera position/angle?
its quite a few years when I learned 3D graphics ...
All of the sites I used are gone now (as usual on the WEB but there are tons of new ones). I am OpenGL user so I recommend to use that. Many of mine students liked NEHE tutorials so look here. Also look at 4x4 transform matrices (homogenous coordinates).
Z-Buffer is automatic in OpenGL just create context with Z-Buffer (all tutorials use it) and call glEnable(GL_DEPTH_TEST);
Face culling (skip the other side of object) is done by glEnable(GL_CULL_FACE); and drawing faces in the same polygon winding (CW or CCW)
Here few related questions:
Understanding 4x4 homogenous transform matrices
3D (software) render pipeline computation
some transform matrices 3x3 and 4x4 insights
how to project points and vectors ... fixed pipeline OpenGL will do it for you
code for inverse 4x4 matrix
this is mine clean OpenGL app example in borland/embarcadero BDS2006 Turbo C++
some projection math
And some good sites to look at (strongly recommend):
transforms
Learning Modern 3D Graphics Programming
GL_PROJECTION matrix abuse
Sorry for that list of links but I think they are relevant and copy their stuff here would be too much. Now back to your question how to render more cubes. I see few options (in OpenGL):
every cube has its own transform matrix
Representing its position and orientation in space then just before rendering each cube change GL_MODELVIEW matrix and draw cube (with the same code for each). If you have too much objects/cubes it will consume big chunk of memory (+16 floats per cube).
every cube is aligned to each other
in this case you need to know just the 3D position (+3 floats per cube) so just do something like this:
glMatrixMode(GL_MODELVIEW); // this store original matrix
glPushMatrix();
glTranslatef(x[i],y[i],z[i]); // position of i-th cube
// here render cube (like glBegin(GL_QUADS); ... or use glDraw... )
glMatrixMode(GL_MODELVIEW); // this restore original matrix
glPopMatrix();
use of shaders
in modern shader pipeline you can use geometry shader to emit cube on receiving point but this is too much for OpenGL beginner. But in this case you would draw just points and the shader will convert them to cubes on GPU which is much faster ...
use VBO or VAO
VAO is vertex array object (list of VBO's)
VBO is vertex buffer object
VBO is basically an array of parameters copied to GPU as one chunk and not by individual calls like glVertex,glColor,glNormal... which is much much faster. This allows you to create model of your space (all cubes) and draw it at once with enough speed unless you hit the GPU/CPU/MEM speed limits
VAO similarly groups more VBOs together so you need to bind just single VAO per object instead of one VBO for each one parameter further reducing the API calls number needed for rendering.