Struct NurbsSurface 

pub struct NurbsSurface {
    pub degree_u: usize,
    pub degree_v: usize,
    pub knots_u: Vec<f64>,
    pub knots_v: Vec<f64>,
    pub control_points: Vec<Vec<Vec4>>,
    /* private fields */
}

A rational B-spline surface.

Invariant: do not mutate the public fields after the surface has been evaluated. The surface memoizes derived data (its analytic carrier, seam closure, projection grids, validation) the first time it is asked, and Clone copies those caches. Editing control_points, knots_* or a degree in place afterwards leaves every later query answering for the OLD geometry. Build a new value with NurbsSurface::new instead (lane K2 audit 2026-10-16: no production path does this today; a test fixture did).

Fields

degree_u: usize

degree_v: usize

knots_u: Vec<f64>

knots_v: Vec<f64>

control_points: Vec<Vec<Vec4>>

Implementations

impl NurbsSurface

pub fn extend_natural( &self, side: SurfaceSide, delta_param: f64, ) -> Result<NurbsSurface, ExtendRefusal>

Continue this surface past one boundary of its parameter square by delta_param, as the analytic continuation of its own terminal Bézier span. See the module comment for the construction and for what survives of the input (everything, over the original domain).

impl NurbsSurface

pub fn new( degree_u: usize, degree_v: usize, knots_u: Vec<f64>, knots_v: Vec<f64>, control_points: Vec<Vec<Vec4>>, ) -> Result<Self, String>

pub fn closed_directions(&self) -> Result<(bool, bool), String>

Whether the surface joins itself along u (first) and v (second): opposite domain edges coincide at three sampled fractions. The 1e-6 threshold matches the historical LINEAR_TOLERANCE * 10 used by the projection and curve×surface intersection modules.

pub fn domain_u(&self) -> Result<[f64; 2], String>

pub fn domain_v(&self) -> Result<[f64; 2], String>

pub fn analytic(&self) -> Option<&AnalyticSurface>

The recognized analytic carrier, if this exact rational patch is a plane or a full revolution quadric/torus. Computed once per instance.

pub fn evaluate_homogeneous(&self, u: f64, v: f64) -> Result<Vec4, String>

pub fn evaluate(&self, u: f64, v: f64) -> Result<Vec3, String>

pub fn evaluate_extended(&self, u: f64, v: f64) -> Result<Vec3, String>

Value beyond the domain (Golovanov §3.15): closed directions wrap cyclically; open directions extend along the boundary tangent plane, with the bilinear corner form when both parameters are outside. Intersection and projection algorithms probe outside the domain, so this is a required capability of every surface.

pub fn derivatives_extended( &self, u: f64, v: f64, derivative_count: usize, ) -> Result<Vec<Vec<Vec3>>, String>

Derivatives beyond the domain (§3.15). The extension is C¹: first derivatives follow the ruled/bilinear extension, second derivatives are taken at the boundary anchor (zero across an extended direction).

pub fn derivatives( &self, u: f64, v: f64, derivative_count: usize, ) -> Result<Vec<Vec<Vec3>>, String>

pub fn normal(&self, u: f64, v: f64) -> Result<Vec3, String>

pub fn principal_curvatures(&self, u: f64, v: f64) -> Result<(f64, f64), String>

Principal curvatures (κ_min, κ_max) at (u, v), signed with respect to the parametrization normal n = Su × Sv / |Su × Sv| via the shape operator I⁻¹·II. Convention check: a cylinder of radius R whose normal points AWAY from the axis has κ = −1/R along the circular direction, so an offset’s regularity factor 1 − d·κ vanishes exactly when an inward offset (d = −R) reaches the axis.

pub fn is_affine(&self) -> Result<bool, String>

Whether this is a genuinely affine degree-1 by degree-1 patch.

A tapered bilinear patch is planar but not affine, so degree alone is insufficient for exact inverse-parameter and integration shortcuts.

pub fn iso_curve_u(&self, u: f64) -> Result<NurbsCurve, String>

pub fn iso_curve_v(&self, v: f64) -> Result<NurbsCurve, String>

Trait Implementations

impl Clone for NurbsSurface

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for NurbsSurface

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for NurbsSurface

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Serialize for NurbsSurface

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.