gnuplot-old/src/interpol.c at pm3d · gnuplot/gnuplot-old · GitHub

Repository navigation

History

1033 lines (888 loc) · 30.2 KB

Raw

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

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

541

542

543

544

545

546

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608

609

610

611

612

613

614

615

616

617

618

619

620

621

622

623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652

653

654

655

656

657

658

659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697

698

699

700

701

702

703

704

705

706

707

708

709

710

711

712

713

714

715

716

717

718

719

720

721

722

723

724

725

726

727

728

729

730

731

732

733

734

735

736

737

738

739

740

741

742

743

744

745

746

747

748

749

750

751

752

753

754

755

756

757

758

759

760

761

762

763

764

765

766

767

768

769

770

771

772

773

774

775

776

777

778

779

780

781

782

783

784

785

786

787

788

789

790

791

792

793

794

795

796

797

798

799

800

801

802

803

804

805

806

807

808

809

810

811

812

813

814

815

816

817

818

819

820

821

822

823

824

825

826

827

828

829

830

831

832

833

834

835

836

837

838

839

840

841

842

843

844

845

846

847

848

849

850

851

852

853

854

855

856

857

858

859

860

861

862

863

864

865

866

867

868

869

870

871

872

873

874

875

876

877

878

879

880

881

882

883

884

885

886

887

888

889

890

891

892

893

894

895

896

897

898

899

900

901

902

903

904

905

906

907

908

909

910

911

912

913

914

915

916

917

918

919

920

921

922

923

924

925

926

927

928

929

930

931

932

933

934

935

936

937

938

939

940

941

942

943

944

945

946

947

948

949

950

951

952

953

954

955

956

957

958

959

960

961

962

963

964

965

966

967

968

969

970

971

972

973

974

975

976

977

978

979

980

981

982

983

984

985

986

987

988

989

990

991

992

993

994

995

996

997

998

999

1000

#ifndef lint

static char *RCSid() { return RCSid("$Id: interpol.c,v 1.13.2.1 2000/05/03 21:26:11 joze Exp $"); }

#endif

/* GNUPLOT - interpol.c */

/*[

* Permission to use, copy, and distribute this software and its

* documentation for any purpose with or without fee is hereby granted,

* provided that the above copyright notice appear in all copies and

* that both that copyright notice and this permission notice appear

* in supporting documentation.

* Permission to modify the software is granted, but not the right to

* distribute the complete modified source code. Modifications are to

* be distributed as patches to the released version. Permission to

* distribute binaries produced by compiling modified sources is granted,

* provided you

* 1. distribute the corresponding source modifications from the

* released version in the form of a patch file along with the binaries,

* 2. add special version identification to distinguish your version

* in addition to the base release version number,

* 3. provide your name and address as the primary contact for the

* support of your modified version, and

* 4. retain our contact information in regard to use of the base

* software.

* Permission to distribute the released version of the source code along

* with corresponding source modifications in the form of a patch file is

* granted with same provisions 2 through 4 for binary distributions.

* This software is provided "as is" without express or implied warranty

* to the extent permitted by applicable law.

]*/

* C-Source file identification Header

* This file belongs to a project which is:

* done 1993 by MGR-Software, Asgard (Lars Hanke)

* written by Lars Hanke

* Contact me via:

* InterNet: mgr@asgard.bo.open.de

* FIDO: Lars Hanke @ 2:243/4802.22 (as long as they keep addresses)

**************************************************************************

* Project: gnuplot

* Module:

* File: interpol.c

* Revisor: Lars Hanke

* Revised: 26/09/93

* Revision: 1.0

**************************************************************************

* LEGAL

* This module is part of gnuplot and distributed under whatever terms

* gnuplot is or will be published, unless exclusive rights are claimed.

* DESCRIPTION

* Supplies 2-D data interpolation and approximation routines

* IMPORTS

* plot.h

* - cp_extend()

* - structs: curve_points, coordval, coordinate

* setshow.h

* - samples, is_log_x, base_log_x, xmin, xmax, autoscale_lx

* - plottypes

* proto.h

* - solve_tri_diag()

* - typedef tri_diag

* EXPORTS

* gen_interp()

* sort_points()

* cp_implode()

* BUGS and TODO

* I would really have liked to use Gershon Elbers contouring code for

* all the stuff done here, but I failed. So I used my own code.

* If somebody is able to consolidate Gershon's code for this purpose

* a lot of gnuplot users would be very happy - due to memory problems.

**************************************************************************

* HISTORY

* Changes:

* Nov 24, 1995 Markus Schuh (M.Schuh@meteo.uni-koeln.de):

* changed the algorithm for csplines

* added algorithm for approximation csplines

* copied point storage and range fix from plot2d.c

* Dec 12, 1995 David Denholm

* oops - at the time this is called, stored co-ords are

* internal (ie maybe log of data) but min/max are in

* user co-ordinates.

* Work with min and max of internal co-ords, and

* check at the end whether external min and max need to

* be increased. (since samples is typically 100 ; we

* dont want to take more logs than necessary)

* Also, need to take into account which axes are active

* Jun 30, 1996 Jens Emmerich

* implemented handling of UNDEFINED points

#include "interpol.h"

#include "alloc.h"

#include "contour.h"

#include "graphics.h"

#include "misc.h"

#include "setshow.h"

#include "util.h"

/* in order to support multiple axes, and to simplify ranging in

* parametric plots, we use arrays to store some things. For 2d plots,

* elements are z=0,y1=1,x1=2,z2=4,y2=5,x2=6 these are given symbolic

* names in plot.h

* IMHO, code is getting too cluttered with repeated chunks of

* code. Some macros to simplify, I hope.

* do { } while(0) is comp.lang.c recommendation for complex macros

* also means that break can be specified as an action, and it will

/* store VALUE or log(VALUE) in STORE, set TYPE as appropriate

* Do OUT_ACTION or UNDEF_ACTION as appropriate

* adjust range provided type is INRANGE (ie dont adjust y if x is outrange

* VALUE must not be same as STORE

#define STORE_AND_FIXUP_RANGE(STORE, VALUE, TYPE, MIN, MAX, AUTO, OUT_ACTION, UNDEF_ACTION)\

do { STORE=VALUE; \

if (TYPE != INRANGE) break; /* dont set y range if x is outrange, for example */ \

if ( VALUE<MIN ) { \

if (AUTO & 1) MIN=VALUE; else { TYPE=OUTRANGE; OUT_ACTION; break; } \

} \

if ( VALUE>MAX ) {\

if (AUTO & 2) MAX=VALUE; else { TYPE=OUTRANGE; OUT_ACTION; } \

} \

} while(0)

#define UPDATE_RANGE(TEST,OLD,NEW,AXIS) \

do { if (TEST) { \

if (log_array[AXIS]) OLD = pow(base_array[AXIS], NEW); else OLD = NEW; \

} \

} while(0)

/* use this instead empty macro arguments to work around NeXT cpp bug */

/* if this fails on any system, we might use ((void)0) */

#define NOOP /* */

#define spline_coeff_size 4

typedef double spline_coeff[spline_coeff_size];

typedef double five_diag[5];

static int next_curve __PROTO((struct curve_points * plot, int *curve_start));

static int num_curves __PROTO((struct curve_points * plot));

static double *cp_binomial __PROTO((int points));

static void eval_bezier __PROTO((struct curve_points * cp, int first_point,

int num_points, double sr, coordval * px,

coordval *py, double *c));

static void do_bezier __PROTO((struct curve_points * cp, double *bc, int first_point, int num_points, struct coordinate * dest));

static int solve_five_diag __PROTO((five_diag m[], double r[], double x[], int n));

static spline_coeff *cp_approx_spline __PROTO((struct curve_points * plot, int first_point, int num_points));

static spline_coeff *cp_tridiag __PROTO((struct curve_points * plot, int first_point, int num_points));

static void do_cubic __PROTO((struct curve_points * plot, spline_coeff * sc, int first_point, int num_points, struct coordinate * dest));

static int compare_points __PROTO((struct coordinate * p1, struct coordinate * p2));

* position curve_start to index the next non-UNDEFINDED point,

* start search at initial curve_start,

* return number of non-UNDEFINDED points from there on,

* if no more valid points are found, curve_start is set

* to plot->p_count and 0 is returned

static int

next_curve(plot, curve_start)

struct curve_points *plot;

int *curve_start;

{

int curve_length;

/* Skip undefined points */

while (*curve_start < plot->p_count

&& plot->points[*curve_start].type == UNDEFINED) {

(*curve_start)++;

};

curve_length = 0;

/* curve_length is first used as an offset, then the correkt # points */

while ((*curve_start) + curve_length < plot->p_count

&& plot->points[(*curve_start) + curve_length].type != UNDEFINED) {

curve_length++;

};

return (curve_length);

}

* determine the number of curves in plot->points, separated by

* UNDEFINED points

static int

num_curves(plot)

struct curve_points *plot;

{

int curves;

int first_point;

int num_points;

first_point = 0;

curves = 0;

while ((num_points = next_curve(plot, &first_point)) > 0) {

curves++;

first_point += num_points;

}

return (curves);

}

* build up a cntr_struct list from curve_points

* this funtion is only used for the alternate entry point to

* Gershon's code and thus commented out

***deleted***

/* HBB 990205: rewrote the 'bezier' interpolation routine,

* to prevent numerical overflow and other undesirable things happening

* for large data files (num_data about 1000 or so), where binomial

* coefficients would explode, and powers of 'sr' (0 < sr < 1) become

* extremely small. Method used: compute logarithms of these

* extremely large and small numbers, and only go back to the

* real numbers once they've cancelled out each other, leaving

* a reasonable-sized one. */

* cp_binomial() computes the binomial coefficients needed for BEZIER stuff

* and stores them into an array which is hooked to sdat.

* (MGR 1992)

static double *

cp_binomial(points)

int points;

{

int e;

e = points; /* well we're going from k=0 to k=p_count-1 */

coeff = (double *) gp_alloc(e * sizeof(double), "bezier coefficients");

n = points - 1;

e = n / 2;

/* HBB 990205: calculate these in 'logarithmic space',

* as they become _very_ large, with growing n (4^n) */

coeff[0] = 0.0;

for (k = 0; k < e; k++) {

coeff[k + 1] = coeff[k] + log(((double) (n - k)) / ((double) (k + 1)));

}

for (k = n; k >= e; k--)

coeff[k] = coeff[n - k];

return (coeff);

}

/* This is a subfunction of do_bezier() for BEZIER style computations.

* It is passed the stepration (STEP/MAXSTEPS) and the addresses of

* the double values holding the next x and y coordinates.

* (MGR 1992)

static void

eval_bezier(cp, first_point, num_points, sr, px, py, c)

struct curve_points *cp;

int first_point; /* where to start in plot->points (to find x-range) */

int num_points; /* to determine end in plot->points */

double sr;

coordval *px;

coordval *py;

double *c;

{

unsigned int n = num_points - 1;

/* HBB 980308: added 'GPHUGE' tag for DOS */

struct coordinate GPHUGE *this_points;

this_points = (cp->points) + first_point;

if (sr == 0.0) {

*px = this_points[0].x;

*py = this_points[0].y;

} else if (sr == 1.0) {

*px = this_points[n].x;

*py = this_points[n].y;

} else {

/* HBB 990205: do calculation in 'logarithmic space',

* to avoid over/underflow errors, which would exactly cancel

* out each other, anyway, in an exact calculation

unsigned int i;

double lx = 0.0, ly = 0.0;

double log_dsr_to_the_n = n * log(1 - sr);

double log_sr_over_dsr = log(sr) - log(1 - sr);

for (i = 0; i <= n; i++) {

double u = exp(c[i] + log_dsr_to_the_n + i * log_sr_over_dsr);

lx += this_points[i].x * u;

ly += this_points[i].y * u;

}

*px = lx;

*py = ly;

}

* generate a new set of coordinates representing the bezier curve and

* set it to the plot

static void

do_bezier(cp, bc, first_point, num_points, dest)

struct curve_points *cp;

double *bc;

int first_point; /* where to start in plot->points */

int num_points; /* to determine end in plot->points */

struct coordinate *dest; /* where to put the interpolated data */

{

int i;

coordval x, y;

int xaxis = cp->x_axis;

int yaxis = cp->y_axis;

/* min and max in internal (eg logged) co-ordinates. We update

* these, then update the external extrema in user co-ordinates

* at the end.

double ixmin, ixmax, iymin, iymax;

double sxmin, sxmax, symin, symax; /* starting values of above */

if (log_array[xaxis]) {

ixmin = sxmin = log(min_array[xaxis]) / log_base_array[xaxis];

ixmax = sxmax = log(max_array[xaxis]) / log_base_array[xaxis];

} else {

ixmin = sxmin = min_array[xaxis];

ixmax = sxmax = max_array[xaxis];

}

if (log_array[yaxis]) {

iymin = symin = log(min_array[yaxis]) / log_base_array[yaxis];

iymax = symax = log(max_array[yaxis]) / log_base_array[yaxis];

} else {

iymin = symin = min_array[yaxis];

iymax = symax = max_array[yaxis];

}

for (i = 0; i < samples; i++) {

eval_bezier(cp, first_point, num_points, (double) i / (double) (samples - 1), &x, &y, bc);

/* now we have to store the points and adjust the ranges */

dest[i].type = INRANGE;

STORE_AND_FIXUP_RANGE(dest[i].x, x, dest[i].type, ixmin, ixmax, auto_array[xaxis], NOOP, continue);

STORE_AND_FIXUP_RANGE(dest[i].y, y, dest[i].type, iymin, iymax, auto_array[yaxis], NOOP, NOOP);

dest[i].xlow = dest[i].xhigh = dest[i].x;

dest[i].ylow = dest[i].yhigh = dest[i].y;

dest[i].z = -1;

}

UPDATE_RANGE(ixmax > sxmax, max_array[xaxis], ixmax, xaxis);

UPDATE_RANGE(ixmin < sxmin, min_array[xaxis], ixmin, xaxis);

UPDATE_RANGE(iymax > symax, max_array[yaxis], iymax, yaxis);

UPDATE_RANGE(iymin < symin, min_array[yaxis], iymin, yaxis);

}

* call contouring routines -- main entry

* it should be like this, but it doesn't run. If you find out why,

* contact me: mgr@asgard.bo.open.de or Lars Hanke 2:243/4802.22@fidonet

* Well, all this had originally been inside contour.c, so maybe links

* to functions and of contour.c are broken.

* ***deleted***

* end of unused entry point to Gershon's code

* Solve five diagonal linear system equation. The five diagonal matrix is

* defined via matrix M, right side is r, and solution X i.e. M * X = R.

* Size of system given in n. Return TRUE if solution exist.

* G. Engeln-Muellges/ F.Reutter:

* "Formelsammlung zur Numerischen Mathematik mit Standard-FORTRAN-Programmen"

* ISBN 3-411-01677-9

* / m02 m03 m04 0 0 0 0 . . . \ / x0 \ / r0 \

* I m11 m12 m13 m14 0 0 0 . . . I I x1 I I r1 I

* I m20 m21 m22 m23 m24 0 0 . . . I * I x2 I = I r2 I

* I 0 m30 m31 m32 m33 m34 0 . . . I I x3 I I r3 I

* . . . . . . . . . . . .

* \ m(n-3)0 m(n-2)1 m(n-1)2 / \x(n-1)/ \r(n-1)/

static int

solve_five_diag(m, r, x, n)

five_diag m[];

double r[], x[];

int n;

{

int i;

five_diag *hv;

hv = (five_diag *) gp_alloc((n + 1) * sizeof(five_diag), "five_diag help vars");

hv[0][0] = m[0][2];

if (hv[0][0] == 0) {

free(hv);

return FALSE;

}

hv[0][1] = m[0][3] / hv[0][0];

hv[0][2] = m[0][4] / hv[0][0];

hv[1][3] = m[1][1];

hv[1][0] = m[1][2] - hv[1][3] * hv[0][1];

if (hv[1][0] == 0) {

free(hv);

return FALSE;

}

hv[1][1] = (m[1][3] - hv[1][3] * hv[0][2]) / hv[1][0];

hv[1][2] = m[1][4] / hv[1][0];

for (i = 2; i <= n - 1; i++) {

hv[i][3] = m[i][1] - m[i][0] * hv[i - 2][1];

hv[i][0] = m[i][2] - m[i][0] * hv[i - 2][2] - hv[i][3] * hv[i - 1][1];

if (hv[i][0] == 0) {

free(hv);

return FALSE;

}

hv[i][1] = (m[i][3] - hv[i][3] * hv[i - 1][2]) / hv[i][0];

hv[i][2] = m[i][4] / hv[i][0];

}

hv[0][4] = 0;

hv[1][4] = r[0] / hv[0][0];

for (i = 1; i <= n - 1; i++) {

hv[i + 1][4] = (r[i] - m[i][0] * hv[i - 1][4] - hv[i][3] * hv[i][4]) / hv[i][0];

}

x[n - 1] = hv[n][4];

x[n - 2] = hv[n - 1][4] - hv[n - 2][1] * x[n - 1];

for (i = n - 3; i >= 0; i--)

x[i] = hv[i + 1][4] - hv[i][1] * x[i + 1] - hv[i][2] * x[i + 2];

free(hv);

return TRUE;

}

* Calculation of approximation cubic splines

* Input: x[i], y[i], weights z[i]

* Returns matrix of spline coefficients

static spline_coeff *

cp_approx_spline(plot, first_point, num_points)

struct curve_points *plot;

int first_point; /* where to start in plot->points */

int num_points; /* to determine end in plot->points */

{

spline_coeff *sc;

five_diag *m;

int xaxis = plot->x_axis;

int yaxis = plot->y_axis;

double *r, *x, *h, *xp, *yp;

/* HBB 980308: added 'GPHUGE' tag */

struct coordinate GPHUGE *this_points;

int i;

sc = (spline_coeff *) gp_alloc((num_points) * sizeof(spline_coeff),

"spline matrix");

if (num_points < 4)

int_error(NO_CARET, "Can't calculate approximation splines, need at least 4 points");

this_points = (plot->points) + first_point;

for (i = 0; i <= num_points - 1; i++)

if (this_points[i].z <= 0)

int_error(NO_CARET, "Can't calculate approximation splines, all weights have to be > 0");

m = (five_diag *) gp_alloc((num_points - 2) * sizeof(five_diag), "spline help matrix");

r = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline right side");

x = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline solution vector");

h = (double *) gp_alloc((num_points - 1) * sizeof(double), "spline help vector");

xp = (double *) gp_alloc((num_points) * sizeof(double), "x pos");

yp = (double *) gp_alloc((num_points) * sizeof(double), "y pos");

/* KB 981107: With logarithmic axis first convert back to linear scale */

if (log_array[xaxis]) {

for (i = 0; i <= num_points - 1; i++)

xp[i] = exp(this_points[i].x * log_base_array[xaxis]);

} else {

for (i = 0; i <= num_points - 1; i++)

xp[i] = this_points[i].x;

}

if (log_array[yaxis]) {

for (i = 0; i <= num_points - 1; i++)

yp[i] = exp(this_points[i].y * log_base_array[yaxis]);

} else {

for (i = 0; i <= num_points - 1; i++)

yp[i] = this_points[i].y;

}

for (i = 0; i <= num_points - 2; i++)

h[i] = xp[i + 1] - xp[i];

/* set up the matrix and the vector */

for (i = 0; i <= num_points - 3; i++) {

r[i] = 3 * ((yp[i + 2] - yp[i + 1]) / h[i + 1]

- (yp[i + 1] - yp[i]) / h[i]);

if (i < 2)

m[i][0] = 0;

else

m[i][0] = 6 / this_points[i].z / h[i - 1] / h[i];

if (i < 1)

m[i][1] = 0;

else

m[i][1] = h[i] - 6 / this_points[i].z / h[i] * (1 / h[i - 1] + 1 / h[i])

- 6 / this_points[i + 1].z / h[i] * (1 / h[i] + 1 / h[i + 1]);

m[i][2] = 2 * (h[i] + h[i + 1])

+ 6 / this_points[i].z / h[i] / h[i]

+ 6 / this_points[i + 1].z * (1 / h[i] + 1 / h[i + 1]) * (1 / h[i] + 1 / h[i + 1])

+ 6 / this_points[i + 2].z / h[i + 1] / h[i + 1];

if (i > num_points - 4)

m[i][3] = 0;

else

m[i][3] = h[i + 1] - 6 / this_points[i + 1].z / h[i + 1] * (1 / h[i] + 1 / h[i + 1])

- 6 / this_points[i + 2].z / h[i + 1] * (1 / h[i + 1] + 1 / h[i + 2]);

if (i > num_points - 5)

m[i][4] = 0;

else

m[i][4] = 6 / this_points[i + 2].z / h[i + 1] / h[i + 2];

}

/* solve the matrix */

if (!solve_five_diag(m, r, x, num_points - 2)) {

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

int_error(NO_CARET, "Can't calculate approximation splines");

}

sc[0][2] = 0;

for (i = 1; i <= num_points - 2; i++)

sc[i][2] = x[i - 1];

sc[num_points - 1][2] = 0;

sc[0][0] = yp[0] + 2 / this_points[0].z / h[0] * (sc[0][2] - sc[1][2]);

for (i = 1; i <= num_points - 2; i++)

sc[i][0] = yp[i] - 2 / this_points[i].z *

(sc[i - 1][2] / h[i - 1]

- sc[i][2] * (1 / h[i - 1] + 1 / h[i])

+ sc[i + 1][2] / h[i]);

sc[num_points - 1][0] = yp[num_points - 1]

- 2 / this_points[num_points - 1].z / h[num_points - 2]

* (sc[num_points - 2][2] - sc[num_points - 1][2]);

for (i = 0; i <= num_points - 2; i++) {

sc[i][1] = (sc[i + 1][0] - sc[i][0]) / h[i]

- h[i] / 3 * (sc[i + 1][2] + 2 * sc[i][2]);

sc[i][3] = (sc[i + 1][2] - sc[i][2]) / 3 / h[i];

}

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

return (sc);

}

* Calculation of cubic splines

* This can be treated as a special case of approximation cubic splines, with

* all weights -> infinity.

* Returns matrix of spline coefficients

static spline_coeff *

cp_tridiag(plot, first_point, num_points)

struct curve_points *plot;

int first_point, num_points;

{

spline_coeff *sc;

tri_diag *m;

int xaxis = plot->x_axis;

int yaxis = plot->y_axis;

double *r, *x, *h, *xp, *yp;

/* HBB 980308: added 'GPHUGE' tag */

struct coordinate GPHUGE *this_points;

int i;

if (num_points < 3)

int_error(NO_CARET, "Can't calculate splines, need at least 3 points");

this_points = (plot->points) + first_point;

sc = (spline_coeff *) gp_alloc((num_points) * sizeof(spline_coeff), "spline matrix");

m = (tri_diag *) gp_alloc((num_points - 2) * sizeof(tri_diag), "spline help matrix");

r = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline right side");

x = (double *) gp_alloc((num_points - 2) * sizeof(double), "spline solution vector");

h = (double *) gp_alloc((num_points - 1) * sizeof(double), "spline help vector");

xp = (double *) gp_alloc((num_points) * sizeof(double), "x pos");

yp = (double *) gp_alloc((num_points) * sizeof(double), "y pos");

/* KB 981107: With logarithmic axis first convert back to linear scale */

if (log_array[xaxis]) {

for (i = 0; i <= num_points - 1; i++)

xp[i] = exp(this_points[i].x * log_base_array[xaxis]);

} else {

for (i = 0; i <= num_points - 1; i++)

xp[i] = this_points[i].x;

}

if (log_array[yaxis]) {

for (i = 0; i <= num_points - 1; i++)

yp[i] = exp(this_points[i].y * log_base_array[yaxis]);

} else {

for (i = 0; i <= num_points - 1; i++)

yp[i] = this_points[i].y;

}

for (i = 0; i <= num_points - 2; i++)

h[i] = xp[i + 1] - xp[i];

/* set up the matrix and the vector */

for (i = 0; i <= num_points - 3; i++) {

r[i] = 3 * ((yp[i + 2] - yp[i + 1]) / h[i + 1]

- (yp[i + 1] - yp[i]) / h[i]);

if (i < 1)

m[i][0] = 0;

else

m[i][0] = h[i];

m[i][1] = 2 * (h[i] + h[i + 1]);

if (i > num_points - 4)

m[i][2] = 0;

else

m[i][2] = h[i + 1];

}

/* solve the matrix */

if (!solve_tri_diag(m, r, x, num_points - 2)) {

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

int_error(NO_CARET, "Can't calculate cubic splines");

}

sc[0][2] = 0;

for (i = 1; i <= num_points - 2; i++)

sc[i][2] = x[i - 1];

sc[num_points - 1][2] = 0;

for (i = 0; i <= num_points - 1; i++)

sc[i][0] = yp[i];

for (i = 0; i <= num_points - 2; i++) {

sc[i][1] = (sc[i + 1][0] - sc[i][0]) / h[i]

- h[i] / 3 * (sc[i + 1][2] + 2 * sc[i][2]);

sc[i][3] = (sc[i + 1][2] - sc[i][2]) / 3 / h[i];

}

free(h);

free(x);

free(r);

free(m);

free(xp);

free(yp);

return (sc);

}

static void

do_cubic(plot, sc, first_point, num_points, dest)

struct curve_points *plot; /* still containes old plot->points */

spline_coeff *sc; /* generated by cp_tridiag */

int first_point; /* where to start in plot->points */

int num_points; /* to determine end in plot->points */

struct coordinate *dest; /* where to put the interpolated data */

{

double xdiff, temp, x, y;

int i, l;

int xaxis = plot->x_axis;

int yaxis = plot->y_axis;

/* HBB 980308: added 'GPHUGE' tag */

struct coordinate GPHUGE *this_points;

/* min and max in internal (eg logged) co-ordinates. We update

* these, then update the external extrema in user co-ordinates

* at the end.

double ixmin, ixmax, iymin, iymax;

double sxmin, sxmax, symin, symax; /* starting values of above */

if (log_array[xaxis]) {

ixmin = sxmin = log(min_array[xaxis]) / log_base_array[xaxis];

ixmax = sxmax = log(max_array[xaxis]) / log_base_array[xaxis];

} else {

ixmin = sxmin = min_array[xaxis];

ixmax = sxmax = max_array[xaxis];

}

if (log_array[yaxis]) {

iymin = symin = log(min_array[yaxis]) / log_base_array[yaxis];

iymax = symax = log(max_array[yaxis]) / log_base_array[yaxis];

} else {

iymin = symin = min_array[yaxis];

iymax = symax = max_array[yaxis];

}

this_points = (plot->points) + first_point;

l = 0;

xdiff = (this_points[num_points - 1].x - this_points[0].x) / (samples - 1);

for (i = 0; i < samples; i++) {

x = this_points[0].x + i * xdiff;

while ((x >= this_points[l + 1].x) && (l < num_points - 2))

l++;

/* KB 981107: With logarithmic x axis the values were converted back to linear */

/* scale before calculating the coefficients. Use exponential for log x values. */

if (log_array[xaxis]) {

temp = exp(x * log_base_array[xaxis]) - exp(this_points[l].x * log_base_array[xaxis]);

y = ((sc[l][3] * temp + sc[l][2]) * temp + sc[l][1]) * temp + sc[l][0];

} else {

temp = x - this_points[l].x;

y = ((sc[l][3] * temp + sc[l][2]) * temp + sc[l][1]) * temp + sc[l][0];

}

/* With logarithmic y axis, we need to convert from linear to log scale now. */

if (log_array[yaxis]) {

if (y > 0.)

y = log(y) / log_base_array[yaxis];

else

y = symin - (symax - symin);

}

dest[i].type = INRANGE;

STORE_AND_FIXUP_RANGE(dest[i].x, x, dest[i].type, ixmin, ixmax, auto_array[xaxis], NOOP, continue);

STORE_AND_FIXUP_RANGE(dest[i].y, y, dest[i].type, iymin, iymax, auto_array[yaxis], NOOP, NOOP);

dest[i].xlow = dest[i].xhigh = dest[i].x;

dest[i].ylow = dest[i].yhigh = dest[i].y;

dest[i].z = -1;

}

UPDATE_RANGE(ixmax > sxmax, max_array[xaxis], ixmax, xaxis);

UPDATE_RANGE(ixmin < sxmin, min_array[xaxis], ixmin, xaxis);

UPDATE_RANGE(iymax > symax, max_array[yaxis], iymax, yaxis);

UPDATE_RANGE(iymin < symin, min_array[yaxis], iymin, yaxis);

}

* This is the main entry point used. As stated in the header, it is fine,

* but I'm not too happy with it.

void

gen_interp(plot)

struct curve_points *plot;

{

spline_coeff *sc;

double *bc;

struct coordinate *new_points;

int i, curves;

int first_point, num_points;

curves = num_curves(plot);

new_points = (struct coordinate *) gp_alloc((samples + 1) * curves * sizeof(struct coordinate), "interpolation table");

first_point = 0;

for (i = 0; i < curves; i++) {

num_points = next_curve(plot, &first_point);

switch (plot->plot_smooth) {

case SMOOTH_CSPLINES:

sc = cp_tridiag(plot, first_point, num_points);

do_cubic(plot, sc, first_point, num_points,

new_points + i * (samples + 1));

free(sc);

break;

case SMOOTH_ACSPLINES:

sc = cp_approx_spline(plot, first_point, num_points);

do_cubic(plot, sc, first_point, num_points,

new_points + i * (samples + 1));

free(sc);

break;

case SMOOTH_BEZIER:

case SMOOTH_SBEZIER:

bc = cp_binomial(num_points);

do_bezier(plot, bc, first_point, num_points,

new_points + i * (samples + 1));

free((char *) bc);

break;

default: /* keep gcc -Wall quiet */

;

}

new_points[(i + 1) * (samples + 1) - 1].type = UNDEFINED;

first_point += num_points;

}

free(plot->points);

plot->points = new_points;

plot->p_max = curves * (samples + 1);

plot->p_count = plot->p_max - 1;

return;

}

* sort_points

* sort data succession for further evaluation by plot_splines, etc.

* This routine is mainly introduced for compilers *NOT* supporting the

* UNIX qsort() routine. You can then easily replace it by more convenient

* stuff for your compiler.

* (MGR 1992)

static int

compare_points(p1, p2)

struct coordinate *p1;

struct coordinate *p2;

{

if (p1->x > p2->x)

return (1);

if (p1->x < p2->x)

return (-1);

return (0);

}

void

sort_points(plot)

struct curve_points *plot;

{

int first_point, num_points;

first_point = 0;

while ((num_points = next_curve(plot, &first_point)) > 0) {

/* Sort this set of points, does qsort handle 1 point correctly? */

qsort((char *) (plot->points + first_point), (size_t)num_points,

sizeof(struct coordinate), (sortfunc) compare_points);

first_point += num_points;

}

return;

}

* cp_implode() if averaging is selected this function computes the new

* entries and shortens the whole thing to the necessary

* size

* MGR Addendum

void

cp_implode(cp)

struct curve_points *cp;

{

int first_point, num_points;

int i, j, k;

double x = 0., y = 0., sux = 0., slx = 0., suy = 0., sly = 0.;

int xaxis = cp->x_axis;

int yaxis = cp->y_axis;

TBOOLEAN all_inrange; /* HBB 20000401: use the right type for this flag */

j = 0;

first_point = 0;

while ((num_points = next_curve(cp, &first_point)) > 0) {

k = 0;

for (i = first_point; i < first_point + num_points; i++) {

if (!k) {

x = cp->points[i].x;

y = cp->points[i].y;

sux = cp->points[i].xhigh;

slx = cp->points[i].xlow;

suy = cp->points[i].yhigh;

sly = cp->points[i].ylow;

all_inrange = (cp->points[i].type == INRANGE);

k = 1;

} else if (cp->points[i].x == x) {

y += cp->points[i].y;

sux += cp->points[i].xhigh;

slx += cp->points[i].xlow;

suy += cp->points[i].yhigh;

sly += cp->points[i].ylow;

if (cp->points[i].type != INRANGE)

all_inrange = FALSE;

k++;

} else {

cp->points[j].x = x;

cp->points[j].y = y /= (double) k;

cp->points[j].xhigh = sux / (double) k;

cp->points[j].xlow = slx / (double) k;

cp->points[j].yhigh = suy / (double) k;

cp->points[j].ylow = sly / (double) k;

/* HBB 20000405: I wanted to use STORE_AND_FIXUP_RANGE

* here, but won't: it assumes we want to modify the

* range, and that the range is given in 'input'

* coordinates. For logarithmic axes, the overhead

* would be larger than the possible gain, so write it

* out explicitly, instead:

* */

cp->points[j].type = INRANGE;

if (! all_inrange) {

if (log_array[xaxis])

x = exp(x * log_base_array[xaxis]);

if (((x < min_array[xaxis]) && !(auto_array[xaxis] & 1))

|| ((x > max_array[xaxis]) && !(auto_array[xaxis] & 2)))

cp->points[j].type = OUTRANGE;

else {

if (log_array[yaxis])

y = exp(y * log_base_array[yaxis]);

if (((y < min_array[yaxis]) && !(auto_array[yaxis] & 1))

|| ((y > max_array[yaxis]) && !(auto_array[yaxis] & 2)))

cp->points[j].type = OUTRANGE;

}

j++; /* next valid entry */

k = 0; /* to read */

i--; /* from this (-> last after for(;;)) entry */

}

if (k) {

View remainder of file in raw view

gnuplot-old/src/interpol.c at pm3d · gnuplot/gnuplot-old · GitHub

Repository navigation

Expand file tree

Breadcrumbs

interpol.c

Latest commit

History

Breadcrumbs

interpol.c

File metadata and controls