Struct SurfaceBounds 

pub struct SurfaceBounds {
    pub du: f64,
    pub dv: f64,
    pub duu: f64,
    pub duv: f64,
    pub dvv: f64,
    pub smooth: bool,
    pub interpolation: [f64; 3],
}

Suprema of a surface’s partial derivatives over a parameter box.

du, dv bound |S_u|, |S_v|; duu, duv, dvv bound the second partials. smooth is false when a B-spline knot line of full multiplicity crosses the box: the second-derivative bounds then hold on each side but not across, and a caller must fall back to a first-order argument there.

Fields

du: f64

sup |S_u|.

dv: f64

sup |S_v|.

duu: f64

sup |S_uu|.

duv: f64

sup |S_uv|.

dvv: f64

sup |S_vv|.

smooth: bool

Whether the second-derivative bounds may be used across the box.

interpolation: [f64; 3]

Coefficients [A, B, C] for linear interpolation over a parameter triangle in the box: every surface point over the triangle is within 1/2 sum_i l_i q(y_i - x), q(d) = A d_u^2 + 2 B |d_u d_v| + C d_v^2, of the triangle spanned by the corners’ surface points.

For a polynomial surface they are duu, duv, dvv. For a rational B-spline S = A / w they are (|A_uu| + R |w_uu|) / w_min and so on (centred numerator, R the active points’ spread): the point l_A / l_w of the homogeneous interpolants is a convex combination of the corners’ surface points, so it lies in their triangle, and S - l_A / l_w = ((A - l_A) - (l_A / l_w)(w - l_w)) / w carries no first-derivative terms, unlike the quotient rule for S_uu.

Trait Implementations

impl Clone for SurfaceBounds

fn clone(&self) -> SurfaceBounds

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for SurfaceBounds

impl Debug for SurfaceBounds

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl PartialEq for SurfaceBounds

fn eq(&self, other: &SurfaceBounds) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for SurfaceBounds