Trait truck_modeling::base::Homogeneous

source · 
pub trait Homogeneous<S>: VectorSpace<Scalar = S>where
    S: BaseFloat,{
    type Point: EuclideanSpace<Scalar = S>;

    fn truncate(self) -> <Self::Point as EuclideanSpace>::Diff;
    fn weight(self) -> S;
    fn from_point(point: Self::Point) -> Self;

    fn from_point_weight(point: Self::Point, weight: S) -> Self { ... }
    fn to_point(self) -> Self::Point { ... }
    fn rat_der(self, der: Self) -> <Self::Point as EuclideanSpace>::Diff { ... }
    fn rat_der2(
        self,
        der: Self,
        der2: Self
    ) -> <Self::Point as EuclideanSpace>::Diff { ... }
    fn rat_cross_der(
        &self,
        uder: Self,
        vder: Self,
        uvder: Self
    ) -> <Self::Point as EuclideanSpace>::Diff { ... }
}
Expand description

Homogeneous coordinate of an Euclidean space and a vector space.

Examples

use truck_base::cgmath64::*;
use truck_base::cgmath_extend_traits::*;
assert_eq!(Vector4::new(8.0, 6.0, 4.0, 2.0).truncate(), Vector3::new(8.0, 6.0, 4.0));
assert_eq!(Vector4::new(8.0, 6.0, 4.0, 2.0).weight(), 2.0);
assert_eq!(Vector4::new(8.0, 6.0, 4.0, 2.0).to_point(), Point3::new(4.0, 3.0, 2.0));
assert_eq!(Vector4::from_point(Point3::new(4.0, 3.0, 2.0)), Vector4::new(4.0, 3.0, 2.0, 1.0));

Required Associated Types§

The point expressed by homogeneous coordinate

Required Methods§

Returns the first dim - 1 components.

Returns the last component.

Returns homogeneous coordinate.

Provided Methods§

Returns homogeneous coordinate from point and weight.

Returns the projection to the plane whose the last component is 1.0.

Returns the derivation of the rational curve.

For a curve c(t) = (c_0(t), c_1(t), c_2(t), c_3(t)), returns the derivation of the projected curve (c_0 / c_3, c_1 / c_3, c_2 / c_3, 1.0).

Arguments
  • self - the point of the curve c(t)
  • der - the derivation c’(t) of the curve
Examples
use truck_base::cgmath64::*;
use truck_base::cgmath_extend_traits::*;
// calculate the derivation at t = 1.5
let t = 1.5;
// the curve: c(t) = (t^2, t^3, t^4, t)
let pt = Vector4::new(t * t, t * t * t, t * t * t * t, t);
// the derivation: c'(t) = (2t, 3t^2, 4t^3, 1)
let der = Vector4::new(2.0 * t, 3.0 * t * t, 4.0 * t * t * t, 1.0);
// the projected curve: \bar{c}(t) = (t, t^2, t^3, 1)
// the derivation of the proj'ed curve: \bar{c}'(t) = (1, 2t, 3t^2, 0)
let ans = Vector3::new(1.0, 2.0 * t, 3.0 * t * t);
assert_eq!(pt.rat_der(der), ans);

Returns the 2nd-ord derivation of the rational curve.

For a curve c(t) = (c_0(t), c_1(t), c_2(t), c_3(t)), returns the 2nd ordered derivation of the projected curve (c_0 / c_3, c_1 / c_3, c_2 / c_3).

Arguments
  • self - the point of the curve c(t)
  • der - the derivation c’(t) of the curve
  • der2 - the 2nd ordered derivation c’’(t) of the curve
Examples
use truck_base::cgmath64::*;
use truck_base::cgmath_extend_traits::*;
// calculate the derivation at t = 1.5
let t = 1.5;
// the curve: c(t) = (t^2, t^3, t^4, t)
let pt = Vector4::new(t * t, t * t * t, t * t * t * t, t);
// the derivation: c'(t) = (2t, 3t^2, 4t^3, 1)
let der = Vector4::new(2.0 * t, 3.0 * t * t, 4.0 * t * t * t, 1.0);
// the 2nd ord. deri.: c''(t) = (2, 6t, 12t^2, 0)
let der2 = Vector4::new(2.0, 6.0 * t, 12.0 * t * t, 0.0);
// the projected curve: \bar{c}(t) = (t, t^2, t^3, 1)
// the derivation of the proj'ed curve: \bar{c}'(t) = (1, 2t, 3t^2, 0)
// the 2nd ord. deri. of the proj'ed curve: \bar{c}''(t) = (0, 2, 6t, 0)
let ans = Vector3::new(0.0, 2.0, 6.0 * t);
assert_eq!(pt.rat_der2(der, der2), ans);

Returns the cross derivation of the rational surface.

For a surface s(u, v) = (s_0(u, v), s_1(u, v), s_2(u, v), s_3(u, v)), returns the derivation of the projected surface (s_0 / s_3, s_1 / s_3, s_2 / s_3) by both u and v.

Arguments
  • self - the point of the surface s(u, v)
  • uder - the u-derivation s_u(u, v) of the surface
  • vder - the v-derivation s_v(u, v) of the surface
  • uvder - the 2nd ordered derivation s_{uv}(u, v) of the surface
Examples
use truck_base::cgmath64::*;
// calculate the derivation at (u, v) = (1.0, 2.0).
let (u, v) = (1.0, 2.0);
// the curve: s(u, v) = (u^3 v^2, u^2 v^3, u v, u)
let pt = Vector4::new(
    u * u * u * v * v,
    u * u * v * v * v,
    u * v,
    u,
);
// the u-derivation: s_u(u, v) = (3u^2 v^2, 2u * v^3, v, 1)
let uder = Vector4::new(
    3.0 * u * u * v * v,
    2.0 * u * v * v * v,
    v,
    1.0,
);
// the v-derivation: s_v(u, v) = (2u^3 v, 3u^2 v^2, u, 0)
let vder = Vector4::new(
    2.0 * u * u * u * v,
    3.0 * u * u * v * v,
    u,
    0.0,
);
// s_{uv}(u, v) = (6u^2 v, 6u v^2, 1, 0)
let uvder = Vector4::new(6.0 * u * u * v, 6.0 * u * v * v, 1.0, 0.0);
// the projected surface: \bar{s}(u, v) = (u^2 v^2, u v^3, v)
// \bar{s}_u(u, v) = (2u v^2, v^3, 0)
// \bar{s}_v(u, v) = (2u^2 v, 3u v^2, 1)
// \bar{s}_{uv}(u, v) = (4uv, 3v^2, 0)
let ans = Vector3::new(4.0 * u * v, 3.0 * v * v, 0.0);
assert_eq!(pt.rat_cross_der(uder, vder, uvder), ans);

Implementors§