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Use circles in triangle as low-curvature construction

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In the process, add a way to build a sphere by offset and curvature.
This commit is contained in:
Aaron Fenyes 2024-09-06 18:57:59 -07:00
parent 3493a798d1
commit ab830b194e
2 changed files with 121 additions and 29 deletions
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15
app-proto/inversive-display/src/engine.rs
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@ -1,5 +1,6 @@
use nalgebra::DVector;
// the sphere with the given center and radius, with inward-pointing normals
pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVector<f64> {
let center_norm_sq = center_x * center_x + center_y * center_y + center_z * center_z;
DVector::from_column_slice(&[
@ -9,4 +10,18 @@ pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVect
0.5 / radius,
0.5 * (center_norm_sq / radius - radius)
])
}
// the sphere of curvature `curv` whose closest point to the origin has position
// `off * dir` and normal `dir`, where `dir` is a unit vector. setting the
// curvature to zero gives a plane
pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f64) -> DVector<f64> {
let norm_sp = 1.0 + off * curv;
DVector::from_column_slice(&[
norm_sp * dir_x,
norm_sp * dir_y,
norm_sp * dir_z,
0.5 * curv,
off * (1.0 + 0.5 * off * curv)
])
}