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tri.p8
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pico-8 cartridge // http://www.pico-8.com
version 8
__lua__
-- 3D engine
model = {}
model.vertices = {
{0, 1, 0},
{-1, -1, 1},
{1, -1, 1},
{-1, -1, -1},
{1, -1, -1},
}
model.triangles = {
{1, 2, 3, 2, nil, nil},
{1, 2, 4, 10, nil, nil},
{1, 3, 5, 8, nil, nil},
{1, 4, 5, 12, nil, nil},
}
scene = {}
scene.camera = {0, 0, -2.5, 64}
function scene_init()
end
function scene_update(frame)
scale = 1.0
scene_transform(0, frame * 0.01, 0, scale, scale, scale)
end
function scene_transform(rx, ry, rz, sx, sy, sz)
local vertices, points = {}, {}
for vertex in all(model.vertices) do
local v = transform_vertex(vertex, rx, ry, rz, sx, sy, sz)
add(vertices, v)
add(points, project(v, scene.camera))
end
model.transformed_vertices = vertices
model.points = points
end
function scene_draw()
-- face depth and normal calculation
for triangle in all(model.triangles) do
local v1 = model.transformed_vertices[triangle[1]]
local v2 = model.transformed_vertices[triangle[2]]
local v3 = model.transformed_vertices[triangle[3]]
local p = {v1[1]-v2[1], v1[2]-v2[2], v1[3]-v2[3]}
local q = {v1[1]-v3[1], v1[2]-v3[2], v1[3]-v3[3]}
triangle[5] = min(v1[3], min(v2[3], v3[3]))
triangle[6] = normalize(cross_product(p, q))
end
-- painter's algorithm
sort(model.triangles, function(t1, t2) return t1[5] < t2[5] end)
-- render
for triangle in all(model.triangles) do
--if dot_product(scene.camera, triangle[6]) < 0 then
local p1 = model.points[triangle[1]]
local p2 = model.points[triangle[2]]
local p3 = model.points[triangle[3]]
rasterize_triangle(p1, p2, p3, triangle[4])
rasterize_mesh(p1, p2, p3, triangle[4])
--end
end
end
function rasterize_mesh(p1, p2, p3, col)
line(p1[1], p1[2], p2[1], p2[2], col)
line(p2[1], p2[2], p3[1], p3[2], col)
line(p1[1], p1[2], p3[1], p3[2], col)
end
-- http://www-users.mat.uni.torun.pl/~wrona/3d_tutor/tri_fillers.html
function rasterize_triangle(p1, p2, p3, col)
-- sort
if p1[2] > p2[2] then
p1, p2 = p2, p1
end
if p1[2] > p3[2] then
p1, p3 = p3, p1
end
if p2[2] > p3[2] then
p2, p3 = p3, p2
end
-- lerp
local dy1 = (p2[2] - p1[2])
local dy2 = (p3[2] - p1[2])
local dy3 = (p3[2] - p2[2])
local dx1, dx2, dx3 = 0, 0, 0
if dy1 > 0 then
dx1 = (p2[1] - p1[1]) / dy1
end
if dy2 > 0 then
dx2 = (p3[1] - p1[1]) / dy2
end
if dy3 > 0 then
dx3 = (p3[1] - p2[1]) / dy3
end
local x1, x2 = p1[1], p1[1]
if dx1 > dx2 then
for y=p1[2],p2[2] do
hline(x1, x2, y, col)
x1 += dx2
x2 += dx1
end
for y=p2[2],p3[2] do
hline(x1, x2, y, col)
x1 += dx2
x2 += dx3
end
else
for y=p1[2],p2[2] do
hline(x1, x2, y, col)
x1 += dx1
x2 += dx2
end
for y=p2[2],p3[2] do
hline(x1, x2, y, col)
x1 += dx3
x2 += dx2
end
end
end
function hline(x1, x2, y, col)
line(x1, y, x2, y, col)
end
function project(vertex, cam)
local mult = cam[4]
local d = (vertex[3]-cam[3])
local x = 64 + (vertex[1]-cam[1]) * mult / d
local y = 64 - (vertex[2]-cam[2]) * mult / d
return {x, y}
end
function transform_vertex(v, rx, ry, rz, sx, sy, sz)
nv = {v[1] * sx, v[2] * sy, v[3] * sz}
nv = rotate_vertex(nv, 1, rx)
nv = rotate_vertex(nv, 2, ry)
return rotate_vertex(nv, 3, rz)
end
function rotate_vertex(v,a,r)
if a==1 then
x,y,z = 3,2,1
elseif a==2 then
x,y,z = 1,3,2
elseif a==3 then
x,y,z = 1,2,3
end
_x = cos(r)*(v[x]) - sin(r) * (v[y])
_y = sin(r)*(v[x]) + cos(r) * (v[y])
nv = {}
nv[x] = _x
nv[y] = _y
nv[z] = v[z]
return nv
end
function cross_product(v1, v2)
return {
v1[2]*v2[3] - v1[3]*v2[2],
v1[3]*v2[1] - v1[1]*v2[3],
v1[1]*v2[2] - v1[2]*v2[1]
}
end
function dot_product(v1, v2)
return v1[1]*v2[1] + v1[2]*v2[2] + v1[3]*v2[3]
end
function normalize(v)
local s = 1 / magnitude(v)
return {v[1] * s, v[2] * s, v[3] * s}
end
function magnitude(v)
return sqrt(dot_product(v, v))
end
function sort(a, greater_than)
for i=1,#a do
local j = i
while j > 1 and greater_than(a[j-1], a[j]) do
a[j],a[j-1] = a[j-1],a[j]
j -= 1
end
end
end
-- main
function _init()
frame = 0
scene_init()
end
function _update()
scene_update(frame)
frame += 1
end
function _draw()
cls()
scene_draw()
end
__gfx__
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__music__
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