3d graphics from scratch -

what minimum configuration program need build 3d graphics scratch, example have sfml working 2d graphics , need implement camera object can move & rotate in space

where start , how implement vector3d -> vector2d conversion functions , other neccessary things

all have is: angles phi, xi, epsilon 1-3 , object can draw on screen following formula

x/y = center.x/y + scale.x/y * dot(point[i], epsilon1/epsilon2) 

but way im transforming "world" axis, not object points

first need implement transform matrix , vector math:

• mathematically compute simple graphics pipeline
• understanding 4x4 homogenous transform matrices

the rest depends on kind of rendering want achieve:

1. boundary polygonal mesh rendering

   this kind of rendering native nowadays gfx cards. need implement buffers for:

   • depth (for filled polygons without z-sorting)
   • screen (to avoid flickering , serves canvas)
   • shadow,stencil,aux (for advanced rendering techniques)

   they have same resolution target rendering area. on top of need implement supported primitives rendering @ least point,line,triangle. see:

   • algorithm fill triangle

   on top of can add textures,shaders , whatever else want ...

2. (back)ray tracing

   this kind of rendering different , current gfx hw not build it. involves implementing ray/primitives intersections computation, snell's law , analytical representation of meshes. way can multi-spectral rendering , more physically accurate effects/processes see:

   • how can render 'atmosphere' on rendering of earth in three.js? hybrid approach #1+#2
   • algorithm 2d raytracer
   • how implement 2d raycasting light effect in glsl
   • multi-band image raster rgb

   the difference between 2d , 3d ray tracer none difference how compute perpendicular vector ...

there different rendering methods volume rendering, hybrid methods , others implementation task oriented , generic description mislead ...