solvr 0.2.0

Advanced computing library for real-world problem solving - optimization, differential equations, interpolation, statistics, and more
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302

//! B-spline surface generic implementation (fully on-device).
//!
//! Uses tensor product of 1D Cox-de Boor bases for evaluation.

use crate::interpolate::error::{InterpolateError, InterpolateResult};
use crate::interpolate::impl_generic::bezier_surface::cross_product_3d;
use crate::interpolate::impl_generic::bspline::compute_basis_matrix;
use crate::interpolate::traits::bspline_surface::BSplineSurface;
use numr::ops::{CompareOps, ScalarOps};
use numr::prelude::DType;
use numr::runtime::{Runtime, RuntimeClient};
use numr::tensor::Tensor;

/// Validate B-spline surface parameters.
fn validate<R: Runtime<DType = DType>>(surface: &BSplineSurface<R>) -> InterpolateResult<()> {
    let shape = surface.control_points.shape();
    if shape.len() != 3 {
        return Err(InterpolateError::InvalidParameter {
            parameter: "control_points".to_string(),
            message: "expected shape [nu, nv, n_dims]".to_string(),
        });
    }
    let nu = shape[0];
    let nv = shape[1];
    let nku = surface.knots_u.shape()[0];
    let nkv = surface.knots_v.shape()[0];

    if nku != nu + surface.degree_u + 1 {
        return Err(InterpolateError::InvalidParameter {
            parameter: "knots_u".to_string(),
            message: format!(
                "expected {} knots_u, got {}",
                nu + surface.degree_u + 1,
                nku
            ),
        });
    }
    if nkv != nv + surface.degree_v + 1 {
        return Err(InterpolateError::InvalidParameter {
            parameter: "knots_v".to_string(),
            message: format!(
                "expected {} knots_v, got {}",
                nv + surface.degree_v + 1,
                nkv
            ),
        });
    }
    Ok(())
}

/// Evaluate a B-spline surface at (u, v) parameter pairs (fully on-device).
pub fn bspline_surface_evaluate_impl<R, C>(
    client: &C,
    surface: &BSplineSurface<R>,
    u: &Tensor<R>,
    v: &Tensor<R>,
) -> InterpolateResult<Tensor<R>>
where
    R: Runtime<DType = DType>,
    C: ScalarOps<R> + CompareOps<R> + RuntimeClient<R>,
{
    validate(surface)?;

    let shape = surface.control_points.shape();
    let nu = shape[0];
    let nv = shape[1];
    let n_dims = shape[2];
    let m = u.shape()[0];

    if m != v.shape()[0] {
        return Err(InterpolateError::ShapeMismatch {
            expected: m,
            actual: v.shape()[0],
            context: "bspline_surface: u and v must have same length".to_string(),
        });
    }

    // B-spline bases
    let basis_u = compute_basis_matrix(client, u, &surface.knots_u, surface.degree_u, nu)?;
    let basis_v = compute_basis_matrix(client, v, &surface.knots_v, surface.degree_v, nv)?;

    // Tensor product: [m, nu*nv]
    let bu_exp = basis_u
        .reshape(&[m, nu, 1])?
        .broadcast_to(&[m, nu, nv])?
        .contiguous()?;
    let bv_exp = basis_v
        .reshape(&[m, 1, nv])?
        .broadcast_to(&[m, nu, nv])?
        .contiguous()?;
    let product = client.mul(&bu_exp, &bv_exp)?;
    let product_flat = product.reshape(&[m, nu * nv])?;

    let cp_flat = surface
        .control_points
        .reshape(&[nu * nv, n_dims])?
        .contiguous()?;
    let result = client.matmul(&product_flat, &cp_flat)?;
    Ok(result)
}

/// Evaluate partial derivatives of a B-spline surface (fully on-device).
///
/// Differentiates control points in u/v directions using forward differences
/// scaled by degree factors, then evaluates the reduced-degree surface.
pub fn bspline_surface_partial_impl<R, C>(
    client: &C,
    surface: &BSplineSurface<R>,
    u: &Tensor<R>,
    v: &Tensor<R>,
    du: usize,
    dv: usize,
) -> InterpolateResult<Tensor<R>>
where
    R: Runtime<DType = DType>,
    C: ScalarOps<R> + CompareOps<R> + RuntimeClient<R>,
{
    if du == 0 && dv == 0 {
        return bspline_surface_evaluate_impl(client, surface, u, v);
    }

    validate(surface)?;

    let shape = surface.control_points.shape();
    let nu = shape[0];
    let nv = shape[1];
    let n_dims = shape[2];
    let m = u.shape()[0];
    let device = client.device();

    if du > surface.degree_u || dv > surface.degree_v {
        return Ok(Tensor::zeros(&[m, n_dims], DType::F64, device));
    }

    // Differentiate du times in u, dv times in v
    let mut diff_cp = surface.control_points.clone();
    let mut deg_u = surface.degree_u;
    let mut cur_nu = nu;
    let mut knots_u = surface.knots_u.clone();

    for _ in 0..du {
        let nku = knots_u.shape()[0];
        let hi = diff_cp.narrow(0, 1, cur_nu - 1)?.contiguous()?;
        let lo = diff_cp.narrow(0, 0, cur_nu - 1)?.contiguous()?;
        let delta = client.sub(&hi, &lo)?;

        // Scale by degree / (knot differences) per row
        // For B-spline derivative: scale factor = deg / (t_{i+deg+1} - t_{i+1})
        let t_hi = knots_u.narrow(0, deg_u + 1, cur_nu - 1)?.contiguous()?;
        let t_lo = knots_u.narrow(0, 1, cur_nu - 1)?.contiguous()?;
        let dt = client.sub(&t_hi, &t_lo)?;

        // Safe division
        let eps = Tensor::full_scalar(&[cur_nu - 1], DType::F64, 1e-300, device);
        let abs_dt = client.abs(&dt)?;
        let dt_safe = client.maximum(&abs_dt, &eps)?;
        let zero = Tensor::zeros(&[cur_nu - 1], DType::F64, device);
        let mask = client.gt(&abs_dt, &zero)?;

        // scale_factors: [cur_nu-1] → [cur_nu-1, 1, 1] for broadcasting
        let cur_nv = diff_cp.shape()[1];
        let scale = client.mul_scalar(
            &client.mul(
                &client.div(&Tensor::ones(&[cur_nu - 1], DType::F64, device), &dt_safe)?,
                &mask,
            )?,
            deg_u as f64,
        )?;
        let scale_broad = scale
            .reshape(&[cur_nu - 1, 1, 1])?
            .broadcast_to(&[cur_nu - 1, cur_nv, n_dims])?
            .contiguous()?;

        diff_cp = client.mul(&delta, &scale_broad)?;

        // Update knots: remove first and last
        knots_u = knots_u.narrow(0, 1, nku - 2)?.contiguous()?;
        deg_u -= 1;
        cur_nu -= 1;
    }

    let mut deg_v = surface.degree_v;
    let mut cur_nv = nv;
    let mut knots_v = surface.knots_v.clone();

    for _ in 0..dv {
        let nkv = knots_v.shape()[0];
        let hi = diff_cp.narrow(1, 1, cur_nv - 1)?.contiguous()?;
        let lo = diff_cp.narrow(1, 0, cur_nv - 1)?.contiguous()?;
        let delta = client.sub(&hi, &lo)?;

        let t_hi = knots_v.narrow(0, deg_v + 1, cur_nv - 1)?.contiguous()?;
        let t_lo = knots_v.narrow(0, 1, cur_nv - 1)?.contiguous()?;
        let dt = client.sub(&t_hi, &t_lo)?;

        let eps = Tensor::full_scalar(&[cur_nv - 1], DType::F64, 1e-300, device);
        let abs_dt = client.abs(&dt)?;
        let dt_safe = client.maximum(&abs_dt, &eps)?;
        let zero = Tensor::zeros(&[cur_nv - 1], DType::F64, device);
        let mask = client.gt(&abs_dt, &zero)?;

        let cur_nu_now = diff_cp.shape()[0];
        let scale = client.mul_scalar(
            &client.mul(
                &client.div(&Tensor::ones(&[cur_nv - 1], DType::F64, device), &dt_safe)?,
                &mask,
            )?,
            deg_v as f64,
        )?;
        let scale_broad = scale
            .reshape(&[1, cur_nv - 1, 1])?
            .broadcast_to(&[cur_nu_now, cur_nv - 1, n_dims])?
            .contiguous()?;

        diff_cp = client.mul(&delta, &scale_broad)?;

        knots_v = knots_v.narrow(0, 1, nkv - 2)?.contiguous()?;
        deg_v -= 1;
        cur_nv -= 1;
    }

    // Evaluate reduced surface
    let deriv_surface = BSplineSurface {
        control_points: diff_cp,
        knots_u,
        knots_v,
        degree_u: deg_u,
        degree_v: deg_v,
    };

    bspline_surface_evaluate_impl(client, &deriv_surface, u, v)
}

/// Compute surface normals at (u, v) parameter pairs (fully on-device).
pub fn bspline_surface_normal_impl<R, C>(
    client: &C,
    surface: &BSplineSurface<R>,
    u: &Tensor<R>,
    v: &Tensor<R>,
) -> InterpolateResult<Tensor<R>>
where
    R: Runtime<DType = DType>,
    C: ScalarOps<R> + CompareOps<R> + RuntimeClient<R>,
{
    let n_dims = surface.control_points.shape()[2];
    if n_dims != 3 {
        return Err(InterpolateError::InvalidParameter {
            parameter: "control_points".to_string(),
            message: "normals require 3D control points".to_string(),
        });
    }

    let du = bspline_surface_partial_impl(client, surface, u, v, 1, 0)?;
    let dv = bspline_surface_partial_impl(client, surface, u, v, 0, 1)?;
    cross_product_3d(client, &du, &dv)
}

#[cfg(test)]
mod tests {
    use super::*;
    use numr::runtime::cpu::{CpuClient, CpuDevice, CpuRuntime};

    fn setup() -> (CpuDevice, CpuClient) {
        let device = CpuDevice::new();
        let client = CpuClient::new(device.clone());
        (device, client)
    }

    #[test]
    fn test_bspline_surface_bilinear() {
        let (device, client) = setup();
        let cp = Tensor::<CpuRuntime>::from_slice(
            &[0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0],
            &[2, 2, 3],
            &device,
        );
        let knots_u = Tensor::<CpuRuntime>::from_slice(&[0.0, 0.0, 1.0, 1.0], &[4], &device);
        let knots_v = Tensor::<CpuRuntime>::from_slice(&[0.0, 0.0, 1.0, 1.0], &[4], &device);

        let surface = BSplineSurface {
            control_points: cp,
            knots_u,
            knots_v,
            degree_u: 1,
            degree_v: 1,
        };

        let u = Tensor::<CpuRuntime>::from_slice(&[0.0, 0.5, 1.0], &[3], &device);
        let v = Tensor::<CpuRuntime>::from_slice(&[0.0, 0.5, 1.0], &[3], &device);
        let result = bspline_surface_evaluate_impl(&client, &surface, &u, &v).unwrap();
        let vals: Vec<f64> = result.to_vec();

        // At (0,0): (0,0,0)
        assert!((vals[0]).abs() < 1e-10);
        // At (0.5, 0.5): (0.5, 0.5, 0)
        assert!((vals[3] - 0.5).abs() < 1e-10);
        assert!((vals[4] - 0.5).abs() < 1e-10);
        // At (1,1): (1,1,0)
        assert!((vals[6] - 1.0).abs() < 1e-10);
        assert!((vals[7] - 1.0).abs() < 1e-10);
    }
}