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use alga::general::Real;
use alga::linear::{Similarity, Transformation};
use na;
use num_traits::Float;
use {BoundingBox, Object, PrimitiveParameters};
#[derive(Clone, Debug)]
pub struct Twister<S: Real> {
object: Box<Object<S>>,
height_scaler: S, value_scaler: S,
bbox: BoundingBox<S>,
}
impl<S: Real + From<f32> + Float + ::num_traits::FloatConst> Object<S> for Twister<S> {
fn approx_value(&self, p: &na::Point3<S>, slack: S) -> S {
let approx = self.bbox.distance(p);
if approx <= slack {
self.object
.approx_value(&self.twist_point(p), slack / self.value_scaler)
* self.value_scaler
} else {
approx
}
}
fn bbox(&self) -> &BoundingBox<S> {
&self.bbox
}
fn set_parameters(&mut self, p: &PrimitiveParameters<S>) {
self.object.set_parameters(p);
}
fn normal(&self, p: &na::Point3<S>) -> na::Vector3<S> {
self.untwist_normal(&self.object.normal(&self.twist_point(&p)), p)
}
}
impl<S: Real + Float + ::num_traits::FloatConst + From<f32>> Twister<S> {
pub fn new(o: Box<Object<S>>, h: S) -> Box<Twister<S>> {
let _2pi: S = S::PI() * From::from(2.);
let mx = Float::max(Float::abs(o.bbox().min.x), Float::abs(o.bbox().max.x));
let my = Float::max(Float::abs(o.bbox().min.y), Float::abs(o.bbox().max.y));
let r = Float::hypot(mx, my);
let tan_a = Float::abs(h) / (_2pi * r);
let one: S = From::from(1f32);
let scaler = tan_a / Float::sqrt(tan_a * tan_a + one);
let bbox = BoundingBox::<S>::new(
&na::Point3::new(-r, -r, o.bbox().min.z),
&na::Point3::new(r, r, o.bbox().max.z),
);
Box::new(Twister {
object: o,
height_scaler: _2pi / h,
value_scaler: scaler,
bbox,
})
}
fn twist_point(&self, p: &na::Point3<S>) -> na::Point3<S> {
let p2 = ::na::Point2::new(p.x, p.y);
let angle = p.z * self.height_scaler;
type Rota<S> = ::na::Rotation<S, ::na::U2>;
let trans = Rota::new(angle);
let rp2 = trans.transform_point(&p2);
na::Point3::new(rp2.x, rp2.y, p.z)
}
fn tilt_normal(&self, normal: na::Vector3<S>, p: &na::Point3<S>) -> na::Vector3<S> {
let radius_v = ::na::Vector2::new(p.x, p.y);
let radius = radius_v.norm();
let radius_v = radius_v / radius;
let tangent_v = ::na::Vector2::new(radius_v.y, -radius_v.x);
let planar_normal = ::na::Vector2::new(normal.x, normal.y);
let tangential_projection = tangent_v.dot(&planar_normal);
let tangential_shear = radius * self.height_scaler;
let mut result = normal;
result.z -= tangential_shear * tangential_projection;
result.normalize()
}
fn untwist_normal(&self, v: &na::Vector3<S>, p: &na::Point3<S>) -> na::Vector3<S> {
let v2 = ::na::Vector2::new(v.x, v.y);
let angle = -p.z * self.height_scaler;
let trans = ::na::Rotation2::new(angle);
let rv2 = trans.rotate_vector(&v2);
self.tilt_normal(na::Vector3::new(rv2.x, rv2.y, v.z), p)
}
}
#[cfg(test)]
mod test {
use super::*;
#[derive(Clone, Debug, PartialEq)]
pub struct MockObject {
value: f64,
normal: na::Vector3<f64>,
bbox: BoundingBox<f64>,
}
impl MockObject {
pub fn new(value: f64, normal: na::Vector3<f64>) -> Box<MockObject> {
Box::new(MockObject {
value,
normal,
bbox: BoundingBox::new(
&na::Point3::new(-1., -1., -100.),
&na::Point3::new(1., 1., 100.),
),
})
}
}
impl Object<f64> for MockObject {
fn approx_value(&self, _: &na::Point3<f64>, _: f64) -> f64 {
self.value
}
fn normal(&self, _: &na::Point3<f64>) -> na::Vector3<f64> {
self.normal
}
fn bbox(&self) -> &BoundingBox<f64> {
&self.bbox
}
}
#[test]
fn simple() {
let m = MockObject::new(10.0, na::Vector3::new(1., 0., 0.));
let t = Twister::new(m, 4.);
assert_relative_eq!(
t.approx_value(&na::Point3::new(0., 0., 0.), 0.),
4.104_846_065_998_354
);
assert_relative_eq!(
t.normal(&na::Point3::new(1., 0., 0.)),
na::Vector3::new(1., 0., 0.)
);
assert_relative_eq!(
t.approx_value(&na::Point3::new(0., 0., 1.), 0.),
4.104_846_065_998_354
);
ulps_eq!(
t.normal(&na::Point3::new(1., 0., 1.)),
na::Vector3::new(0., -0.537_029_272_146_315_1, 0.843_563_608_068_768_6)
);
assert_relative_eq!(
t.approx_value(&na::Point3::new(0., 0., 2.), 0.),
4.104_846_065_998_354
);
assert_relative_eq!(
t.normal(&na::Point3::new(1., 0., 2.)),
na::Vector3::new(-1., 0., 0.)
);
assert_relative_eq!(
t.approx_value(&na::Point3::new(0., 0., 3.), 0.),
4.104_846_065_998_354
);
assert_relative_eq!(
t.normal(&na::Point3::new(1., 0., 3.)),
na::Vector3::new(0., 0.537_029_272_146_315_1, 0.843_563_608_068_768_6)
);
assert_relative_eq!(
t.approx_value(&na::Point3::new(0., 0., 4.), 0.),
4.104_846_065_998_354
);
assert_relative_eq!(
t.normal(&na::Point3::new(1., 0., 4.)),
na::Vector3::new(
1.,
0.000_000_000_000_000_244_929_359_829_470_64,
0.000_000_000_000_000_384_734_138_744_357_95
)
);
}
}