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ddd.p8
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pico-8 cartridge // http://www.pico-8.com
version 8
__lua__
-- math
function vec_add(v1, v2)
return {v1[1]+v2[1], v1[2]+v2[2], v1[3]+v2[3]}
end
function vec_sub(v1, v2)
return {v1[1]-v2[1], v1[2]-v2[2], v1[3]-v2[3]}
end
function vec_cross(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 vec_dot(v1, v2)
return v1[1]*v2[1] + v1[2]*v2[2] + v1[3]*v2[3]
end
function vec_normalize(v)
local s = 1 / vec_magnitude(v)
return {v[1]*s, v[2]*s, v[3]*s}
end
function vec_magnitude(v)
return sqrt(vec_dot(v, v))
end
function vec_transform(v, m)
return {
v[1]*m[1] + v[2]*m[2] + v[3]*m[3],
v[1]*m[4] + v[2]*m[5] + v[3]*m[6],
v[1]*m[7] + v[2]*m[8] + v[3]*m[9]
}
end
function mat_mul(m1, m2)
local r = {}
for j=1,9,3 do
for i=1,3 do
add(r, m2[i]*m1[j] + m2[i+3]*m1[j+1] + m2[i+6]*m1[j+2])
end
end
return r
end
function mat_rot(x, y, z)
local cx, sx = cos(x), sin(x)
local cy, sy = cos(y), sin(y)
local cz, sz = cos(z), sin(z)
return {
(cx*cy)+((-sx*-sz)*-sy), ((-sx*cz)), (cx*sy)+((-sx*-sz)*cy),
(sx*cy)+((cx*-sz)*-sy), ((cx*cz)), (sx*sy)+((cx*-sz)*cy),
(cz*-sy), sz, (cz*cy),
}
end
function mat_transpose(m)
return {
m[1], m[4], m[7],
m[2], m[5], m[8],
m[3], m[6], m[9],
}
end
function mat_view(pos, lat, roll)
local u, v, p
p = vec_normalize(vec_sub(lat, pos))
if p[1] == 0 and p[3] == 0 then
v = {-p[2], 0, 0}
else
v = {0, 1, 0}
end
u = vec_normalize(vec_cross(p, v))
v = vec_cross(p, v)
local cz, sz = cos(z), sin(z)
return {
cz*u[1]+sz*v[2], cz*u[2]+sz*v[2], cz*u[3]+sz*v[3],
sz*u[1]+cz*v[2], sz*u[2]+cz*v[2], sz*u[3]+cz*v[3],
p[1], p[2], p[3]
}
end
function mat_scale(x, y, z)
return {
x, 0, 0,
0, y, 0,
0, 0, z
}
end
-- mesh generation
-- http://blog.andreaskahler.com/2009/06/creating-icosphere-mesh-in-code.html
function icosahedron()
local t = (1 + sqrt(5)) * .5;
ico = {}
ico.vertices = {
{pos={-1, t, 0}},
{pos={ 1, t, 0}},
{pos={-1, -t, 0}},
{pos={ 1, -t, 0}},
{pos={ 0, -1, t}},
{pos={ 0, 1, t}},
{pos={ 0, -1, -t}},
{pos={ 0, 1, -t}},
{pos={ t, 0, -1}},
{pos={ t, 0, 1}},
{pos={-t, 0, -1}},
{pos={-t, 0, 1}},
}
ico.faces = {
{vertices={0, 11, 5}},
{vertices={0, 5, 1}},
{vertices={0, 1, 7}},
{vertices={0, 7, 10}},
{vertices={0, 10, 11}},
{vertices={1, 5, 9}},
{vertices={5, 11, 4}},
{vertices={11, 10, 2}},
{vertices={10, 7, 6}},
{vertices={7, 1, 8}},
{vertices={3, 9, 4}},
{vertices={3, 4, 2}},
{vertices={3, 2, 6}},
{vertices={3, 6, 8}},
{vertices={3, 8, 9}},
{vertices={4, 9, 5}},
{vertices={2, 4, 11}},
{vertices={6, 2, 10}},
{vertices={8, 6, 7}},
{vertices={9, 8, 1}},
}
local palette = {12, 7, 8}
for idx, face in pairs(ico.faces) do
face.vertices[1] += 1
face.vertices[2] += 1
face.vertices[3] += 1
face.col = 8+rnd(6)
end
return ico
end
function torus(rings, sides, inner_radius, outer_radius)
local model = {}
model.vertices = {}
for u=0,rings-1 do
local rho = u / rings
for v=0,sides-1 do
local theta = v / sides
local x = (outer_radius + inner_radius * cos(theta)) * cos(rho)
local y = (outer_radius + inner_radius * cos(theta)) * sin(rho)
local z = inner_radius * sin(theta)
add(model.vertices, {pos={x, y, z}})
end
end
-- todo fix
model.faces = {}
for v=0,rings-1 do
local v1 = v+1
for u=0,sides-1 do
local u1 = u+1
local lt = u + v * (sides)
local rt = u1 + v * (sides)
local lb = u + v1 * (sides)
local rb = u1 + v1 * (sides)
add(model.faces, {vertices={lt+1, rt+1, lb+1}, col=7})
add(model.faces, {vertices={rt+1, rb+1, lb+1}, col=8})
end
end
return model
end
-- 3D engine
-- model = {}
-- model.vertices = {
-- {pos={0, 1, 0}, },
-- {pos={-1, -1, 1}, },
-- {pos={1, -1, 1}, },
-- {pos={-1, -1, -1} },
-- {pos={1, -1, -1}, },
-- }
-- model.faces = {
-- {vertices={1, 2, 3}, col=2},
-- {vertices={1, 2, 4}, col=10},
-- {vertices={1, 3, 5}, col=8},
-- {vertices={1, 4, 5}, col=12},
-- }
model = icosahedron()
--model = torus(6, 5, 10, 20)
model.pos = {0, 0, 0}
scene = {}
scene.camera = {
pos={0, 0, 10},
lat={0, 0, 0},
roll=0
}
scene.old_camera = {0, 0, -2.5, 64}
function scene_init()
-- precalc face normals
for face in all(model.faces) do
local v1 = model.vertices[face.vertices[1]].pos
local v2 = model.vertices[face.vertices[2]].pos
local v3 = model.vertices[face.vertices[3]].pos
local p = vec_sub(v1, v2)
local q = vec_sub(v1, v3)
face.normal = vec_normalize(vec_cross(p, q))
end
end
function scene_update(frame)
angle = frame * 0.005
scale = 1 --+ 0.2*sin(frame * 0.05)
model_transform(frame, 0, angle, angle, 1, scale, 1)
end
function model_transform(frame, rx, ry, rz, sx, sy, sz)
local view = mat_view(scene.camera.pos, scene.camera.lat, scene.camera.roll)
local rotation = mat_rot(rx, ry, rz)
local translation = vec_transform(vec_sub(model.pos, scene.camera.pos), view)
local cam_pos_inv = vec_transform(vec_sub(scene.camera.pos, model.pos), mat_transpose(rotation))
--local sm = mat_scale(sx, sy, sz)
local transformation = mat_mul(view, rotation)
for face in all(model.faces) do
local los = vec_sub(model.vertices[face.vertices[1]].pos, cam_pos_inv)
face.visible = vec_dot(los, face.normal) < 0
if face.visible then
for idx=1,3 do
local vertex = model.vertices[face.vertices[idx]]
if vertex.cnt != frame then
vertex.trn = vec_add(vec_transform(vertex.pos, transformation), translation)
local iz = 1/vertex.trn[3]
vertex.prj = {
x=64 + vertex.trn[1]*iz*128,
y=64 + vertex.trn[2]*iz*128,
z=iz
}
vertex.cnt = frame
end
end
local tv1 = model.vertices[face.vertices[1]].trn
local tv2 = model.vertices[face.vertices[2]].trn
local tv3 = model.vertices[face.vertices[3]].trn
face.depth = (tv1[3]+tv2[3]+tv3[3])/3
else
face.depth = 0
end
end
end
faces_drawn = 0
function scene_draw()
-- painter's algorithm
sort(model.faces, function(t1, t2) return t1.depth < t2.depth end)
-- render
faces_drawn = 0
for i=1,#model.faces do
local face = model.faces[i]
if face.visible then
local p1 = model.vertices[face.vertices[1]].prj
local p2 = model.vertices[face.vertices[2]].prj
local p3 = model.vertices[face.vertices[3]].prj
rasterize_triangle(p1, p2, p3, face.col)
rasterize_mesh(p1, p2, p3, 7)
faces_drawn += 1
end
end
end
function rasterize_mesh(p1, p2, p3, col)
line(p1.x, p1.y, p2.x, p2.y, col)
line(p2.x, p2.y, p3.x, p3.y, col)
line(p1.x, p1.y, p3.x, p3.y, col)
end
function rasterize_triangle(p1, p2, p3, col)
if p1.y > p2.y then p1, p2 = p2, p1 end
if p1.y > p3.y then p1, p3 = p3, p1 end
if p2.y > p3.y then p2, p3 = p3, p2 end
local dx1 = (p2.x-p1.x) / (p2.y-p1.y)
local dx2 = (p3.x-p2.x) / (p3.y-p2.y)
local dx3 = (p3.x-p1.x) / (p3.y-p1.y)
local x1, x2 = p1.x, p1.x
for y=p1.y,p2.y do
hline(x1, x2, y, col)
x1 += dx3
x2 += dx1
end
x2 = p2.x
for y=p2.y,p3.y do
hline(x1, x2, y, col)
x1 += dx3
x2 += dx2
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=x, y=y}
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()
color(7)
print(frame)
print(faces_drawn)
end
__gfx__
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__music__
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