vec3 Spine::C(Radians t)
{
float x = (a + b * cos_(q * t)) * cos_(p * t);
float y = (a + b * cos_(q * t)) * sin_(p * t);
float z = b * sin_(q * t);
return {x, y, z};
}
vec3 Spine::A(Radians t)
{
vec3 d = T(t);
float ax = -p * d.y + b * q * (p * sin_(q * t) * sin_(p * t) - q * cos_(q * t) * cos_(p * t));
float ay = p * d.x - b * q * (p * sin_(q * t) * cos_(p * t) + q * cos_(q * t) * sin_(p * t));
float az = -b * q * q * sin_(q * t);
return {ax, ay, az};
}
vec3 Spine::T(Radians t)
{
// in CSE we trust
vec3 c = C(t);
float dx = -p * c.y - b * q * sin_(q * t) * cos_(p * t);
float dy = p * c.x - b * q * sin_(q * t) * sin_(p * t);
float dz = b * q * cos_(q * t);
return {dx, dy, dz};
}
void Spine::update_mesh()
{
if (!dirty_mesh)
return;
int N = n * p * q;
int M = m;
while ((N + 1) * (M + 1) >= 65536)
N--;
dirty_mesh = false;
vec3 points[(N + 1) * (M + 1)];
vec3 norms[(N + 1) * (M + 1)];
vec4 params[(N + 1) * (M + 1)];
struct sv2
{
unsigned short a, b;
};
sv2 quad_indices[N * (M + 1)];
for (int i = 0; i <= N; ++i)
{
Turns t_(i, N);
Radians t = t_;
vec3 Ct = C(t);
vec3 Bt = B(t);
norm3(Bt);
vec3 Nt = this->N(t);
norm3(Nt);
for (int j = 0; j <= M; ++j)
{
Turns u_(j, M);
Radians u = u_;
params[i * (M + 1) + j] = {t_.value() * q, u_.value(), 0, 1};
norms[i * (M + 1) + j] = s * cos_(u) * Bt + r * sin_(u) * Nt;
norm3(norms[i * (M + 1) + j]);
points[i * (M + 1) + j] = Ct + r * cos_(u) * Bt + s * sin_(u) * Nt;
if (i == N)
continue;
quad_indices[i * (M + 1) + j] = {
(unsigned short)(i * (M + 1) + j),
(unsigned short)((i + 1) * (M + 1) + j),
};
}
}
char filename[256];
sprintf(filename, "data/spiral-%.10e,%.10e,%.10e,%.10e-%d,%d,%d,%d.mesh",
a, b, r, s,
p, q, N, M);
FILE *fp = fopen(filename, "w");
fprintf(fp, "textures:\n");
fprintf(fp, " ambient: data/earthlights1k.bmp\n");
fprintf(fp, " diffuse: data/earthmap1k.bmp\n");
fprintf(fp, " specular: data/earthspec1k.bmp\n");
fprintf(fp, "\nvertices:\n");
for (int i = 0; i < (N + 1) * (M + 1); ++i)
{
auto p = vec4(points[i], 1.0f);
auto t = params[i];
auto n = vec4(norms[i], 1.0f);
fprintf(fp, " - position: [%.10e, %.10e, %.10e, %.10e]\n", p.x, p.y, p.z, p.w);
fprintf(fp, " texture: [%.10e, %.10e, %.10e, %.10e]\n", t.x * this->q, t.y, t.z, t.w);
fprintf(fp, " normal: [%.10e, %.10e, %.10e, %.10e]\n", n.x, n.y, n.z, n.w);
}
fprintf(fp, "\nfaces:\n");
for (int j = 1; j < N * (M + 1); ++j)
{
ivec3 f1 =
{
quad_indices[j - 1].a,
quad_indices[j - 1].b,
quad_indices[j].a,
};
ivec3 f2 =
{
quad_indices[j - 1].b,
quad_indices[j].b,
quad_indices[j].a,
};
fprintf(fp, " - [%d, %d, %d]\n", f1.x, f1.y, f1.z);
fprintf(fp, " - [%d, %d, %d]\n", f2.x, f2.y, f2.z);
}
fclose(fp);
glBindBuffer(GL_ARRAY_BUFFER, mesh_points);
glBufferData(GL_ARRAY_BUFFER,
sizeof(points), points,
GL_STATIC_DRAW);
glBindBuffer(GL_ARRAY_BUFFER, mesh_norms);
glBufferData(GL_ARRAY_BUFFER,
sizeof(norms), norms,
GL_STATIC_DRAW);
glBindBuffer(GL_ARRAY_BUFFER, mesh_params);
glBufferData(GL_ARRAY_BUFFER,
sizeof(params), params,
GL_STATIC_DRAW);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, mesh_indices);
glBufferData(GL_ELEMENT_ARRAY_BUFFER,
sizeof(quad_indices), quad_indices,
GL_STATIC_DRAW);
}
int16_t cos_(int16_t angle){
return sin_(angle+90);
}
int main()
{
int x = 1;
printf("sin(%d) = %.2f\n",x,sin_(x));
}
