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contour.c
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1991-07-18
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/* GNUPLOT - contour.c */
/*
* Copyright (C) 1986, 1987, 1990, 1991 Thomas Williams, Colin Kelley
*
* 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 modified code. Modifications are to be distributed
* as patches to released version.
*
* This software is provided "as is" without express or implied warranty.
*
*
* AUTHORS
*
* Original Software:
* Gershon Elber
*
* Send your comments or suggestions to
* pixar!info-gnuplot@sun.com.
* This is a mailing list; to join it send a note to
* pixar!info-gnuplot-request@sun.com.
* Send bug reports to
* pixar!bug-gnuplot@sun.com.
*/
#include <stdio.h>
#include "plot.h"
#define DEFAULT_NUM_OF_ZLEVELS 10 /* Some dflt values (setable via flags). */
#define DEFAULT_NUM_APPROX_PTS 5
#define DEFAULT_BSPLINE_ORDER 3
#define MAX_NUM_OF_ZLEVELS 100 /* Some max. values (setable via flags). */
#define MAX_NUM_APPROX_PTS 100
#define MAX_BSPLINE_ORDER 10
#define INTERP_NOTHING 0 /* Kind of interpolations on contours. */
#define INTERP_CUBIC 1 /* Cubic spline interp. */
#define APPROX_BSPLINE 2 /* Bspline interpolation. */
#define ACTIVE 1 /* Status of edges at certain Z level. */
#define INACTIVE 2
#define OPEN_CONTOUR 1 /* Contour kinds. */
#define CLOSED_CONTOUR 2
#define EPSILON 1e-5 /* Used to decide if two float are equal. */
#define INFINITY 1e10
#ifndef TRUE
#define TRUE -1
#define FALSE 0
#endif
#define DEFAULT_NUM_CONTOURS 10
#define MAX_POINTS_PER_CNTR 100
#define SHIFT_Z_EPSILON 0.000301060 /* Dec. change of poly bndry hit.*/
#define abs(x) ((x) > 0 ? (x) : (-(x)))
#define sqr(x) ((x) * (x))
typedef double tri_diag[3]; /* Used to allocate the tri-diag matrix. */
typedef double table_entry[4]; /* Cubic spline interpolation 4 coef. */
struct vrtx_struct {
double X, Y, Z; /* The coordinates of this vertex. */
struct vrtx_struct *next; /* To chain lists. */
};
struct edge_struct {
struct poly_struct *poly[2]; /* Each edge belongs to up to 2 polygons. */
struct vrtx_struct *vertex[2]; /* The two extreme points of this vertex. */
struct edge_struct *next; /* To chain lists. */
int status, /* Status flag to mark edges in scanning at certain Z level. */
boundary; /* True if this edge is on the boundary. */
};
struct poly_struct {
struct edge_struct *edge[3]; /* As we do triangolation here... */
struct poly_struct *next; /* To chain lists. */
};
struct cntr_struct { /* Contours are saved using this struct list. */
double X, Y; /* The coordinates of this vertex. */
struct cntr_struct *next; /* To chain lists. */
};
static int test_boundary; /* If TRUE look for contours on boundary first. */
static struct gnuplot_contours *contour_list = NULL;
static double crnt_cntr[MAX_POINTS_PER_CNTR * 2];
static int crnt_cntr_pt_index = 0;
static double contour_level = 0.0;
static table_entry *hermit_table = NULL; /* Hold hermite table constants. */
static int num_of_z_levels = DEFAULT_NUM_OF_ZLEVELS; /* # Z contour levels. */
static int num_approx_pts = DEFAULT_NUM_APPROX_PTS;/* # pts per approx/inter.*/
static int bspline_order = DEFAULT_BSPLINE_ORDER; /* Bspline order to use. */
static int interp_kind = INTERP_NOTHING; /* Linear, Cubic interp., Bspline. */
static void gen_contours();
static int update_all_edges();
static struct cntr_struct *gen_one_contour();
static struct cntr_struct *trace_contour();
static struct cntr_struct *update_cntr_pt();
static int fuzzy_equal();
static void gen_triangle();
static struct vrtx_struct *gen_vertices();
static struct edge_struct *gen_edges_middle();
static struct edge_struct *gen_edges();
static struct poly_struct *gen_polys();
static void free_contour();
static void put_contour();
static put_contour_nothing();
static put_contour_cubic();
static put_contour_bspline();
static calc_tangent();
static int count_contour();
static complete_spline_interp();
static calc_hermit_table();
static hermit_interp();
static prepare_spline_interp();
static int solve_tri_diag();
static gen_bspline_approx();
static double fetch_knot();
static eval_bspline();
/*
* Entry routine to this whole set of contouring module.
*/
struct gnuplot_contours *contour(num_isolines, iso_lines,
ZLevels, approx_pts, kind, order1)
int num_isolines;
struct iso_curve *iso_lines;
int ZLevels, approx_pts, kind, order1;
{
int i;
struct poly_struct *p_polys, *p_poly;
struct edge_struct *p_edges, *p_edge;
struct vrtx_struct *p_vrts, *p_vrtx;
double x_min, y_min, z_min, x_max, y_max, z_max, z, dz, z_scale = 1.0;
num_of_z_levels = ZLevels;
num_approx_pts = approx_pts;
bspline_order = order1 - 1;
interp_kind = kind;
contour_list = NULL;
if (interp_kind == INTERP_CUBIC) calc_hermit_table();
gen_triangle(num_isolines, iso_lines, &p_polys, &p_edges, &p_vrts,
&x_min, &y_min, &z_min, &x_max, &y_max, &z_max);
dz = (z_max - z_min) / (num_of_z_levels+1);
/* Step from z_min+dz upto z_max-dz in num_of_z_levels times. */
z = z_min + dz;
crnt_cntr_pt_index = 0;
for (i=0; i<num_of_z_levels; i++, z += dz) {
contour_level = z;
gen_contours(p_edges, z + dz * SHIFT_Z_EPSILON, x_min, x_max,
y_min, y_max);
}
/* Free all contouring related temporary data. */
while (p_polys) {
p_poly = p_polys -> next;
free (p_polys);
p_polys = p_poly;
}
while (p_edges) {
p_edge = p_edges -> next;
free (p_edges);
p_edges = p_edge;
}
while (p_vrts) {
p_vrtx = p_vrts -> next;
free (p_vrts);
p_vrts = p_vrtx;
}
if (interp_kind == INTERP_CUBIC) free(hermit_table);
return contour_list;
}
/*
* Adds another point to the currently build contour.
*/
add_cntr_point(x, y)
double x, y;
{
int index;
if (crnt_cntr_pt_index >= MAX_POINTS_PER_CNTR-1) {
index = crnt_cntr_pt_index - 1;
end_crnt_cntr();
crnt_cntr[0] = crnt_cntr[index * 2];
crnt_cntr[1] = crnt_cntr[index * 2 + 1];
crnt_cntr_pt_index = 1; /* Keep the last point as first of this one. */
}
crnt_cntr[crnt_cntr_pt_index * 2] = x;
crnt_cntr[crnt_cntr_pt_index * 2 + 1] = y;
crnt_cntr_pt_index++;
}
/*
* Done with current contour - create gnuplot data structure for it.
*/
end_crnt_cntr()
{
int i;
struct gnuplot_contours *cntr = (struct gnuplot_contours *)
alloc(sizeof(struct gnuplot_contours),
"gnuplot_contour");
cntr->coords = (struct coordinate *) alloc(sizeof(struct coordinate) *
crnt_cntr_pt_index,
"contour coords");
for (i=0; i<crnt_cntr_pt_index; i++) {
cntr->coords[i].x = crnt_cntr[i * 2];
cntr->coords[i].y = crnt_cntr[i * 2 + 1];
cntr->coords[i].z = contour_level;
}
cntr->num_pts = crnt_cntr_pt_index;
cntr->next = contour_list;
contour_list = cntr;
crnt_cntr_pt_index = 0;
}
/*
* Generates all contours by tracing the intersecting triangles.
*/
static void gen_contours(p_edges, z_level, x_min, x_max, y_min, y_max)
struct edge_struct *p_edges;
double z_level, x_min, x_max, y_min, y_max;
{
int num_active, /* Number of edges marked ACTIVE. */
contour_kind; /* One of OPEN_CONTOUR, CLOSED_CONTOUR. */
struct cntr_struct *p_cntr;
num_active = update_all_edges(p_edges, z_level); /* Do pass 1. */
test_boundary = TRUE; /* Start to look for contour on boundaries. */
while (num_active > 0) { /* Do Pass 2. */
/* Generate One contour (and update MumActive as needed): */
p_cntr = gen_one_contour(p_edges, z_level, &contour_kind, &num_active);
put_contour(p_cntr, z_level, x_min, x_max, y_min, y_max,
contour_kind); /* Emit it in requested format. */
}
}
/*
* Does pass 1, or marks the edges which are active (crosses this z_level)
* as ACTIVE, and the others as INACTIVE:
* Returns number of active edges (marked ACTIVE).
*/
static int update_all_edges(p_edges, z_level)
struct edge_struct *p_edges;
double z_level;
{
int count = 0;
while (p_edges) {
if (((p_edges -> vertex[0] -> Z >= z_level) &&
(p_edges -> vertex[1] -> Z <= z_level)) ||
((p_edges -> vertex[1] -> Z >= z_level) &&
(p_edges -> vertex[0] -> Z <= z_level))) {
p_edges -> status = ACTIVE;
count++;
}
else p_edges -> status = INACTIVE;
p_edges = p_edges -> next;
}
return count;
}
/*
* Does pass 2, or find one complete contour out of the triangolation data base:
* Returns a pointer to the contour (as linked list), contour_kind is set to
* one of OPEN_CONTOUR, CLOSED_CONTOUR, and num_active is updated.
*/
static struct cntr_struct *gen_one_contour(p_edges, z_level, contour_kind,
num_active)
struct edge_struct *p_edges;
double z_level;
int *contour_kind, *num_active;
{
struct edge_struct *pe_temp;
if (test_boundary) { /* Look for something to start with on boundary: */
pe_temp = p_edges;
while (pe_temp) {
if ((pe_temp -> status == ACTIVE) && (pe_temp -> boundary)) break;
pe_temp = pe_temp -> next;
}
if (!pe_temp) test_boundary = FALSE;/* No more contours on boundary. */
else {
*contour_kind = OPEN_CONTOUR;
return trace_contour(pe_temp, z_level, num_active, *contour_kind);
}
}
if (!test_boundary) { /* Look for something to start with inside: */
pe_temp = p_edges;
while (pe_temp) {
if ((pe_temp -> status == ACTIVE) && (!(pe_temp -> boundary)))
break;
pe_temp = pe_temp -> next;
}
if (!pe_temp) {
*num_active = 0;
return NULL;
}
else {
*contour_kind = CLOSED_CONTOUR;
return trace_contour(pe_temp, z_level, num_active, *contour_kind);
}
}
return NULL; /* We should never be here, but lint... */
}
/*
* Search the data base along a contour starts at the edge pe_start until
* a boundary edge is detected or until we close the loop back to pe_start.
* Returns a linked list of all the points on the contour
* Also decreases num_active by the number of points on contour.
*/
static struct cntr_struct *trace_contour(pe_start, z_level, num_active,
contour_kind)
struct edge_struct *pe_start;
double z_level;
int *num_active, contour_kind;
{
int i, in_middle; /* If TRUE the z_level is in the middle of edge. */
struct cntr_struct *p_cntr, *pc_tail;
struct edge_struct *p_edge = pe_start, *p_next_edge;
struct poly_struct *p_poly, *PLastpoly = NULL;
/* Generate the header of the contour - the point on pe_start. */
if (contour_kind == OPEN_CONTOUR) pe_start -> status = INACTIVE;
(*num_active)--;
p_cntr = pc_tail = update_cntr_pt(pe_start, z_level, &in_middle);
if (!in_middle) {
return NULL;
}
do {
/* Find polygon to continue (Not where we came from - PLastpoly): */
if (p_edge -> poly[0] == PLastpoly) p_poly = p_edge -> poly[1];
else p_poly = p_edge -> poly[0];
p_next_edge = NULL; /* In case of error, remains NULL. */
for (i=0; i<3; i++) /* Test the 3 edges of the polygon: */
if (p_poly -> edge[i] != p_edge)
if (p_poly -> edge[i] -> status == ACTIVE)
p_next_edge = p_poly -> edge[i];
if (!p_next_edge) {
pc_tail -> next = NULL;
free_contour(p_cntr);
return NULL;
}
p_edge = p_next_edge;
PLastpoly = p_poly;
p_edge -> status = INACTIVE;
(*num_active)--;
pc_tail -> next = update_cntr_pt(p_edge, z_level, &in_middle);
if (!in_middle) {
pc_tail -> next = NULL;
free_contour(p_cntr);
return NULL;
}
pc_tail = pc_tail -> next;
}
while ((pe_start != p_edge) && (!p_edge -> boundary));
pc_tail -> next = NULL;
return p_cntr;
}
/*
* Allocates one contour location and update it to to correct position
* according to z_level and edge p_edge. if z_level is found to be at
* one of the extreme points nothing is allocated (NULL is returned)
* and in_middle is set to FALSE.
*/
static struct cntr_struct *update_cntr_pt(p_edge, z_level, in_middle)
struct edge_struct *p_edge;
double z_level;
int *in_middle;
{
double t;
struct cntr_struct *p_cntr;
t = (z_level - p_edge -> vertex[0] -> Z) /
(p_edge -> vertex[1] -> Z - p_edge -> vertex[0] -> Z);
if (fuzzy_equal(t, 1.0) || fuzzy_equal(t, 0.0)) {
*in_middle = FALSE;
return NULL;
}
else {
*in_middle = TRUE;
p_cntr = (struct cntr_struct *) alloc(sizeof(struct cntr_struct),
"contour cntr_struct");
p_cntr -> X = p_edge -> vertex[1] -> X * t +
p_edge -> vertex[0] -> X * (1-t);
p_cntr -> Y = p_edge -> vertex[1] -> Y * t +
p_edge -> vertex[0] -> Y * (1-t);
return p_cntr;
}
}
/*
* Simple routine to decide if two real values are equal by simply
* calculating the relative/absolute error between them (< EPSILON).
*/
static int fuzzy_equal(x, y)
double x, y;
{
if (abs(x) > EPSILON) /* Calculate relative error: */
return (abs((x - y) / x) < EPSILON);
else /* Calculate absolute error: */
return (abs(x - y) < EPSILON);
}
/*
* Generate the triangles.
* Returns the lists (vrtxs edges & polys) via pointers to their heads.
*/
static void gen_triangle(num_isolines, iso_lines, p_polys, p_edges,
p_vrts, x_min, y_min, z_min, x_max, y_max, z_max)
int num_isolines;
struct iso_curve *iso_lines;
struct poly_struct **p_polys;
struct edge_struct **p_edges;
struct vrtx_struct **p_vrts;
double *x_min, *y_min, *z_min, *x_max, *y_max, *z_max;
{
int i, grid_x_max = iso_lines->p_count;
struct vrtx_struct *p_vrtx1, *p_vrtx2, *pv_temp;
struct edge_struct *p_edge1, *p_edge2, *pe_tail1, *pe_tail2, *pe_temp,
*p_edge_middle, *pe_m_tail;
struct poly_struct *p_poly, *pp_tail;
*p_polys = NULL;
*p_edges = NULL;
*p_vrts = NULL;
*z_min = INFINITY;
*y_min = INFINITY;
*x_min = INFINITY;
*z_max = -INFINITY;
*y_max = -INFINITY;
*x_max = -INFINITY;
/* Read 1st row. */
p_vrtx1 = gen_vertices(grid_x_max, iso_lines->points,
x_min, y_min, z_min, x_max, y_max, z_max);
*p_vrts = p_vrtx1;
/* Gen. its edges.*/
pe_temp = p_edge1 = gen_edges(grid_x_max, p_vrtx1, &pe_tail1);
for (i = 1; i < grid_x_max; i++) {/* Mark one side of edges as boundary. */
pe_temp -> poly[1] = NULL;
pe_temp = pe_temp -> next;
}
for (i = 1; i < num_isolines; i++) { /* Read next column and gen. polys. */
iso_lines = iso_lines->next;
/* Get row into list. */
p_vrtx2 = gen_vertices(grid_x_max, iso_lines->points,
x_min, y_min, z_min, x_max, y_max, z_max);
/* Generate its edges. */
p_edge2 = gen_edges(grid_x_max, p_vrtx2, &pe_tail2);
/* Generate edges from one vertex list to the other one: */
p_edge_middle = gen_edges_middle(grid_x_max, p_vrtx1, p_vrtx2,
&pe_m_tail);
/* Now we can generate the polygons themselves (triangles). */
p_poly = gen_polys(grid_x_max, p_edge1, p_edge_middle, p_edge2,
&pp_tail);
pe_tail1 -> next = (*p_edges); /* Chain new edges to main list. */
pe_m_tail -> next = p_edge1;
*p_edges = p_edge_middle;
pe_tail1 = pe_tail2;
p_edge1 = p_edge2;
pv_temp = p_vrtx2;
while (pv_temp -> next) pv_temp = pv_temp -> next;
pv_temp -> next = *p_vrts;
*p_vrts = p_vrtx1 = p_vrtx2;
pp_tail -> next = (*p_polys); /* Chain new polys to main list. */
*p_polys = p_poly;
}
pe_temp = p_edge1;
for (i = 1; i < grid_x_max; i++) {/* Mark one side of edges as boundary. */
pe_temp -> poly[0] = NULL;
pe_temp = pe_temp -> next;
}
pe_tail1 -> next = (*p_edges); /* Chain last edges list to main list. */
*p_edges = p_edge1;
/* Update the boundary flag, saved in each edge, and update indexes: */
pe_temp = (*p_edges);
i = 1;
while (pe_temp) {
pe_temp -> boundary = (!(pe_temp -> poly[0])) ||
(!(pe_temp -> poly[1]));
pe_temp = pe_temp -> next;
}
}
/*
* Handles grid_x_max 3D points (One row) and generate linked list for them.
*/
static struct vrtx_struct *gen_vertices(grid_x_max, points,
x_min, y_min, z_min, x_max, y_max, z_max)
int grid_x_max;
struct coordinate *points;
double *x_min, *y_min, *z_min, *x_max, *y_max, *z_max;
{
int i;
struct vrtx_struct *p_vrtx, *pv_tail, *pv_temp;
for (i=0; i<grid_x_max; i++) {/* Get a point and generate the structure. */
pv_temp = (struct vrtx_struct *) alloc(sizeof(struct vrtx_struct),
"contour vertex");
pv_temp -> X = points[i].x;
pv_temp -> Y = points[i].y;
pv_temp -> Z = points[i].z;
if (pv_temp -> X > *x_max) *x_max = pv_temp -> X; /* Update min/max. */
if (pv_temp -> Y > *y_max) *y_max = pv_temp -> Y;
if (pv_temp -> Z > *z_max) *z_max = pv_temp -> Z;
if (pv_temp -> X < *x_min) *x_min = pv_temp -> X;
if (pv_temp -> Y < *y_min) *y_min = pv_temp -> Y;
if (pv_temp -> Z < *z_min) *z_min = pv_temp -> Z;
if (i == 0) /* First vertex in row: */
p_vrtx = pv_tail = pv_temp;
else {
pv_tail -> next = pv_temp; /* Stick new record as last one. */
pv_tail = pv_tail -> next; /* And continue to last record. */
}
}
pv_tail -> next = NULL;
return p_vrtx;
}
/*
* Combines N vertices in pair to form N-1 edges.
* Returns pointer to the edge list (pe_tail will point on last edge in list).
*/
static struct edge_struct *gen_edges(grid_x_max, p_vrtx, pe_tail)
int grid_x_max;
struct vrtx_struct *p_vrtx;
struct edge_struct **pe_tail;
{
int i;
struct edge_struct *p_edge, *pe_temp;
for (i=0; i<grid_x_max-1; i++) { /* Generate grid_x_max-1 edges: */
pe_temp = (struct edge_struct *) alloc(sizeof(struct edge_struct),
"contour edge");
pe_temp -> vertex[0] = p_vrtx; /* First vertex of edge. */
p_vrtx = p_vrtx -> next; /* Skip to next vertex. */
pe_temp -> vertex[1] = p_vrtx; /* Second vertex of edge. */
if (i == 0) /* First edge in row: */
p_edge = (*pe_tail) = pe_temp;
else {
(*pe_tail) -> next = pe_temp; /* Stick new record as last one. */
*pe_tail = (*pe_tail) -> next; /* And continue to last record. */
}
}
(*pe_tail) -> next = NULL;
return p_edge;
}
/*
* Combines 2 lists of N vertices each into edge list:
* The dots (.) are the vertices list, and the . . . .
* edges generated are alternations of vertical edges |\ |\ |\ |
* (|) and diagonal ones (\). | \| \| \|
* A pointer to edge list (alternate | , \) is returned . . . .
* Note this list will have (2*grid_x_max-1) edges (pe_tail points on last
* record).
*/
static struct edge_struct *gen_edges_middle(grid_x_max, p_vrtx1, p_vrtx2,
pe_tail)
int grid_x_max;
struct vrtx_struct *p_vrtx1, *p_vrtx2;
struct edge_struct **pe_tail;
{
int i;
struct edge_struct *p_edge, *pe_temp;
/* Gen first (|). */
pe_temp = (struct edge_struct *) alloc(sizeof(struct edge_struct),
"contour edge");
pe_temp -> vertex[0] = p_vrtx2; /* First vertex of edge. */
pe_temp -> vertex[1] = p_vrtx1; /* Second vertex of edge. */
p_edge = (*pe_tail) = pe_temp;
/* Advance in vrtx list grid_x_max-1 times, and gen. 2 edges /| for each.*/
for (i=0; i<grid_x_max-1; i++) {
/* The / edge. */
pe_temp = (struct edge_struct *) alloc(sizeof(struct edge_struct),
"contour edge");
pe_temp -> vertex[0] = p_vrtx1; /* First vertex of edge. */
pe_temp -> vertex[1] = p_vrtx2 -> next; /* Second vertex of edge. */
(*pe_tail) -> next = pe_temp; /* Stick new record as last one. */
*pe_tail = (*pe_tail) -> next; /* And continue to last record. */
/* The | edge. */
pe_temp = (struct edge_struct *) alloc(sizeof(struct edge_struct),
"contour edge");
pe_temp -> vertex[0] = p_vrtx2 -> next; /* First vertex of edge. */
pe_temp -> vertex[1] = p_vrtx1 -> next; /* Second vertex of edge. */
(*pe_tail) -> next = pe_temp; /* Stick new record as last one. */
*pe_tail = (*pe_tail) -> next; /* And continue to last record. */
p_vrtx1 = p_vrtx1 -> next; /* Skip to next vertices in both lists. */
p_vrtx2 = p_vrtx2 -> next;
}
(*pe_tail) -> next = NULL;
return p_edge;
}
/*
* Combines 3 lists of edges into triangles:
* 1. p_edge1: Top horizontal edge list: -----------------------
* 2. p_edge_middge: middle edge list: |\ |\ |\ |\ |\ |\ |
* | \| \| \| \| \| \|
* 3. p_edge2: Bottom horizontal edge list: -----------------------
* Note that p_edge1/2 lists has grid_x_max-1 edges, while p_edge_middle has
* (2*grid_x_max-1) edges.
* The routine simple scans the two list Upper 1 Lower
* and generate two triangle upper one ---- | \
* and lower one from the lists: 0\ |2 0| \1
* (Nums. are edges order in polys) \ | ----
* The routine returns a pointer to a 2
* polygon list (pp_tail points on last polygon). 1
* -----------
* In addition, the edge lists are updated - | \ 0 |
* each edge has two pointers on the two | \ |
* (one active if boundary) polygons which 0|1 0\1 0|1
* uses it. These two pointer to polygons | \ |
* are named: poly[0], poly[1]. The diagram | 1 \ |
* on the right show how they are used for the -----------
* upper and lower polygons. 0
*/
static struct poly_struct *gen_polys(grid_x_max, p_edge1, p_edge_middle,
p_edge2, pp_tail)
int grid_x_max;
struct edge_struct *p_edge1, *p_edge_middle, *p_edge2;
struct poly_struct **pp_tail;
{
int i;
struct poly_struct *p_poly, *pp_temp;
p_edge_middle -> poly[0] = NULL; /* Its boundary! */
/* Advance in vrtx list grid_x_max-1 times, and gen. 2 polys for each. */
for (i=0; i<grid_x_max-1; i++) {
/* The Upper. */
pp_temp = (struct poly_struct *) alloc(sizeof(struct poly_struct),
"contour poly");
/* Now update polys about its edges, and edges about the polygon. */
pp_temp -> edge[0] = p_edge_middle -> next;
p_edge_middle -> next -> poly[1] = pp_temp;
pp_temp -> edge[1] = p_edge1;
p_edge1 -> poly[0] = pp_temp;
pp_temp -> edge[2] = p_edge_middle -> next -> next;
p_edge_middle -> next -> next -> poly[0] = pp_temp;
if (i == 0) /* Its first one in list: */
p_poly = (*pp_tail) = pp_temp;
else {
(*pp_tail) -> next = pp_temp;
*pp_tail = (*pp_tail) -> next;
}
/* The Lower. */
pp_temp = (struct poly_struct *) alloc(sizeof(struct poly_struct),
"contour poly");
/* Now update polys about its edges, and edges about the polygon. */
pp_temp -> edge[0] = p_edge_middle;
p_edge_middle -> poly[1] = pp_temp;
pp_temp -> edge[1] = p_edge_middle -> next;
p_edge_middle -> next -> poly[0] = pp_temp;
pp_temp -> edge[2] = p_edge2;
p_edge2 -> poly[1] = pp_temp;
(*pp_tail) -> next = pp_temp;
*pp_tail = (*pp_tail) -> next;
p_edge1 = p_edge1 -> next;
p_edge2 = p_edge2 -> next;
p_edge_middle = p_edge_middle -> next -> next;
}
p_edge_middle -> poly[1] = NULL; /* Its boundary! */
(*pp_tail) -> next = NULL;
return p_poly;
}
/*
* Calls the (hopefully) desired interpolation/approximation routine.
*/
static void put_contour(p_cntr, z_level, x_min, x_max, y_min, y_max, contr_kind)
struct cntr_struct *p_cntr;
double z_level, x_min, x_max, y_min, y_max;
int contr_kind;
{
if (!p_cntr) return; /* Nothing to do if it is empty contour. */
switch (interp_kind) {
case INTERP_NOTHING: /* No interpolation/approximation. */
put_contour_nothing(p_cntr);
break;
case INTERP_CUBIC: /* Cubic spline interpolation. */
put_contour_cubic(p_cntr, z_level, x_min, x_max, y_min, y_max,
contr_kind);
break;
case APPROX_BSPLINE: /* Bspline approximation. */
put_contour_bspline(p_cntr, z_level, x_min, x_max, y_min, y_max,
contr_kind);
break;
}
free_contour(p_cntr);
}
/*
* Simply puts contour coordinates in order with no interpolation or
* approximation.
*/
static put_contour_nothing(p_cntr)
struct cntr_struct *p_cntr;
{
while (p_cntr) {
add_cntr_point(p_cntr -> X, p_cntr -> Y);
p_cntr = p_cntr -> next;
}
end_crnt_cntr();
}
/*
* Find Complete Cubic Spline Interpolation.
*/
static put_contour_cubic(p_cntr, z_level, x_min, x_max, y_min, y_max,
contr_kind)
struct cntr_struct *p_cntr;
double z_level, x_min, x_max, y_min, y_max;
int contr_kind;
{
int num_pts, i;
double tx1, ty1, tx2, ty2; /* Tangents at end points. */
struct cntr_struct *pc_temp;
num_pts = count_contour(p_cntr); /* Number of points in contour. */
if (num_pts > 2) { /* Take into account 3 points in tangent estimation. */
calc_tangent(3, p_cntr -> X, p_cntr -> next -> X,
p_cntr -> next -> next -> X,
p_cntr -> Y, p_cntr -> next -> Y,
p_cntr -> next -> next -> Y, &tx1, &ty1);
pc_temp = p_cntr;
for (i=3; i<num_pts; i++) pc_temp = pc_temp -> next;/* Go to the end.*/
calc_tangent(3, pc_temp -> next -> next -> X,
pc_temp -> next -> X, pc_temp -> X,
pc_temp -> next -> next -> Y,
pc_temp -> next -> Y, pc_temp -> Y, &tx2, &ty2);
tx2 = (-tx2); /* Inverse the vector as we need opposite direction. */
ty2 = (-ty2);
}
/* If following (num_pts > 1) is TRUE then exactly 2 points in contour. */
else if (num_pts > 1) {/* Take into account 2 points in tangent estimat. */
calc_tangent(2, p_cntr -> X, p_cntr -> next -> X, 0.0,
p_cntr -> Y, p_cntr -> next -> Y, 0.0, &tx1, &ty1);
calc_tangent(2, p_cntr -> next -> X, p_cntr -> X, 0.0,
p_cntr -> next -> Y, p_cntr -> Y, 0.0, &tx2, &ty2);
tx2 = (-tx2); /* Inverse the vector as we need opposite direction. */
ty2 = (-ty2);
}
else return; /* Only one point (???) - ignore it. */
switch (contr_kind) {
case OPEN_CONTOUR:
break;
case CLOSED_CONTOUR:
tx1 = tx2 = (tx1 + tx2) / 2.0; /* Make tangents equal. */
ty1 = ty2 = (ty1 + ty2) / 2.0;
break;
}
complete_spline_interp(p_cntr, num_pts, 0.0, 1.0, tx1, ty1, tx2, ty2);
end_crnt_cntr();
}
/*
* Find Bspline approximation for this data set.
* Uses global variable num_approx_pts to determine number of samples per
* interval, where the knot vector intervals are assumed to be uniform, and
* Global variable bspline_order for the order of Bspline to use.
*/
static put_contour_bspline(p_cntr, z_level, x_min, x_max, y_min, y_max,
contr_kind)
struct cntr_struct *p_cntr;
double z_level, x_min, x_max, y_min, y_max;
int contr_kind;
{
int num_pts, i, order = bspline_order;
struct cntr_struct *pc_temp;
num_pts = count_contour(p_cntr); /* Number of points in contour. */
if (num_pts < 2) return; /* Cannt do nothing if empty or one points! */
/* Order must be less than number of points in curve - fix it if needed. */
if (order > num_pts - 1) order = num_pts - 1;
gen_bspline_approx(p_cntr, num_pts, order, contr_kind);
end_crnt_cntr();
}
/*
* Estimate the tangents according to the n last points where n might be
* 2 or 3 (if 2 onlt x1, x2).
*/
static calc_tangent(n, x1, x2, x3, y1, y2, y3, tx, ty)
int n;
double x1, x2, x3, y1, y2, y3, *tx, *ty;
{
double v1[2], v2[2], v1_magnitude, v2_magnitude;
switch (n) {
case 2:
*tx = (x2 - x1) * 0.3;
*ty = (y2 - y1) * 0.3;
break;
case 3:
v1[0] = x2 - x1; v1[1] = y2 - y1;
v2[0] = x3 - x2; v2[1] = y3 - y2;
v1_magnitude = sqrt(sqr(v1[0]) + sqr(v1[1]));
v2_magnitude = sqrt(sqr(v2[0]) + sqr(v2[1]));
*tx = (v1[0] / v1_magnitude) - (v2[0] / v2_magnitude) * 0.1;
*tx *= v1_magnitude * 0.1; /* Make tangent less than magnitude. */
*ty = (v1[1] / v1_magnitude) - (v2[1] / v2_magnitude) * 0.1;
*ty *= v1_magnitude * 0.1; /* Make tangent less than magnitude. */
break;
default: /* Should not happen! */
(*ty) = 0.1;
*tx = 0.1;
break;
}
}
/*
* Free all elements in the contour list.
*/
static void free_contour(p_cntr)
struct cntr_struct *p_cntr;
{
struct cntr_struct *pc_temp;
while (p_cntr) {
pc_temp = p_cntr;
p_cntr = p_cntr -> next;
free((char *) pc_temp);
}
}
/*
* Counts number of points in contour.
*/
static int count_contour(p_cntr)
struct cntr_struct *p_cntr;
{
int count = 0;
while (p_cntr) {
count++;
p_cntr = p_cntr -> next;
}
return count;
}
/*
* Interpolate given point list (defined via p_cntr) using Complete
* Spline interpolation.
*/
static complete_spline_interp(p_cntr, n, t_min, t_max, tx1, ty1, tx2, ty2)
struct cntr_struct *p_cntr;
int n;
double t_min, t_max, tx1, ty1, tx2, ty2;
{
double dt, *tangents_x, *tangents_y;
int i;
tangents_x = (double *) alloc((unsigned) (sizeof(double) * n),
"contour c_s_intr");
tangents_y = (double *) alloc((unsigned) (sizeof(double) * n),
"contour c_s_intr");
if (n > 1) prepare_spline_interp(tangents_x, tangents_y, p_cntr, n,
t_min, t_max, tx1, ty1, tx2, ty2);
else {
free((char *) tangents_x);
free((char *) tangents_y);
return;
}
dt = (t_max-t_min)/(n-1);
add_cntr_point(p_cntr -> X, p_cntr -> Y); /* First point. */
for (i=0; i<n-1; i++) {
hermit_interp(p_cntr -> X, p_cntr -> Y,
tangents_x[i], tangents_y[i],
p_cntr -> next -> X, p_cntr -> next -> Y,
tangents_x[i+1], tangents_y[i+1], dt);
p_cntr = p_cntr -> next;
}
free((char *) tangents_x);
free((char *) tangents_y);
}
/*
* Routine to calculate intermidiate value of the Hermit Blending function:
* This routine should be called only ONCE at the beginning of the program.
*/
static calc_hermit_table()
{
int i;
double t, dt;
hermit_table = (table_entry *) alloc ((unsigned) (sizeof(table_entry) *
(num_approx_pts + 1)),
"contour hermit table");
t = 0;
dt = 1.0/num_approx_pts;
for (i=0; i<=num_approx_pts; i++) {
hermit_table[i][0] = (t-1)*(t-1)*(2*t+1); /* h00. */
hermit_table[i][1] = t*t*(-2*t+3); /* h10. */
hermit_table[i][2] = t*(t-1)*(t-1); /* h01. */
hermit_table[i][3] = t*t*(t-1); /* h11. */
t = t + dt;
}
}
/*
* Routine to generate an hermit interpolation between two points given as
* two InterpStruct structures. Assume hermit_table is already calculated.
* Currently the points generated are printed to stdout as two reals (X, Y).
*/
static hermit_interp(x1, y1, tx1, ty1, x2, y2, tx2, ty2, dt)
double x1, y1, tx1, ty1, x2, y2, tx2, ty2, dt;
{
int i;
double x, y, vec_size, tang_size;
tx1 *= dt; ty1 *= dt; /* Normalize the tangents according to param. t. */
tx2 *= dt; ty2 *= dt;
/* Normalize the tangents so that their magnitude will be 1/3 of the */
/* segment length. This tumb rule guaranteed no cusps or loops! */
/* Note that this normalization keeps continuity to be G1 (but not C1). */
vec_size = sqrt(sqr(x1 - x2) + sqr(y2 - y1));
tang_size = sqrt(sqr(tx1) + sqr(ty1)); /* Normalize T1. */
if (tang_size * 3 > vec_size) {
tx1 *= vec_size / (tang_size * 3);
ty1 *= vec_size / (tang_size * 3);
}
tang_size = sqrt(sqr(tx2) + sqr(ty2)); /* Normalize T2. */
if (tang_size * 3 > vec_size) {
tx2 *= vec_size / (tang_size * 3);
ty2 *= vec_size / (tang_size * 3);
}
for (i=1; i<=num_approx_pts; i++) { /* Note we start from 1 - first */
x = hermit_table[i][0] * x1 + /* point is not printed as it is */
hermit_table[i][1] * x2 + /* redundent (last on last section). */
hermit_table[i][2] * tx1 +
hermit_table[i][3] * tx2;
y = hermit_table[i][0] * y1 +
hermit_table[i][1] * y2 +
hermit_table[i][2] * ty1 +
hermit_table[i][3] * ty2;
add_cntr_point(x, y);
}
}
/*
* Routine to Set up the 3*N mat for solve_tri_diag routine used in the
* Complete Spline Interpolation. Returns TRUE of calc O.K.
* Gets the points list in p_cntr (Of length n) and with tangent vectors tx1,
* ty1 at starting point and tx2, ty2 and end point.
*/
static prepare_spline_interp(tangents_x, tangents_y, p_cntr, n, t_min, t_max,
tx1, ty1, tx2, ty2)
double tangents_x[], tangents_y[];
struct cntr_struct *p_cntr;
int n;
double t_min, t_max, tx1, ty1, tx2, ty2;
{
int i;
double *r, t, dt;
tri_diag *m; /* The tri-diagonal matrix is saved here. */
struct cntr_struct *p;
m = (tri_diag *) alloc((unsigned) (sizeof(tri_diag) * n),
"contour tri_diag");
r = (double *) alloc((unsigned) (sizeof(double) * n),
"contour tri_diag2");
n--;
p = p_cntr;
m[0][0] = 0.0; m[0][1] = 1.0; m[0][2] = 0.0;
m[n][0] = 0.0; m[n][1] = 1.0; m[n][2] = 0.0;
r[0] = tx1; /* Set start tangent. */
r[n] = tx2; /* Set end tangent. */
t = t_min;
dt = (t_max-t_min)/n;
for (i=1; i<n; i++) {
t = t + dt;
m[i][0] = dt;
m[i][2] = dt;
m[i][1] = 2 * (m[i][0] + m[i][2]);
r[i] = m[i][0] * ((p -> next -> X) - (p -> X)) / m[i][2]
+ m[i][2] * ((p -> next -> next -> X) -
(p -> next -> X)) / m[i][0];
r[i] *= 3.0;
p = p -> next;
}
if (!solve_tri_diag(m, r, tangents_x, n+1)) { /* Find the X(t) tangents. */
free((char *) m);
free((char *) r);
int_error("Cannt interpolate X using complete splines", NO_CARET);
}
p = p_cntr;
m[0][0] = 0.0; m[0][1] = 1.0; m[0][2] = 0.0;
m[n][0] = 0.0; m[n][1] = 1.0; m[n][2] = 0.0;
r[0] = ty1; /* Set start tangent. */
r[n] = ty2; /* Set end tangent. */
t = t_min;
dt = (t_max-t_min)/n;
for (i=1; i<n; i++) {
t = t + dt;
m[i][0] = dt;
m[i][2] = dt;
m[i][1] = 2 * (m[i][0] + m[i][2]);
r[i] = m[i][0] * ((p -> next -> Y) - (p -> Y)) / m[i][2]
+ m[i][2] * ((p -> next -> next -> Y) -
(p -> next -> Y)) / m[i][0];
r[i] *= 3.0;
p = p -> next;
}
if (!solve_tri_diag(m, r, tangents_y, n+1)) { /* Find the Y(t) tangents. */
free((char *) m);
free((char *) r);
int_error("Cannt interpolate Y using complete splines", NO_CARET);
}
free((char *) m);
free((char *) r);
}
/*
* Solve tri diagonal linear system equation. The tri 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.
*/
static int solve_tri_diag(m, r, x, n)
tri_diag m[];
double r[], x[];
int n;
{
int i;
double t;
for (i=1; i<n; i++) { /* Eliminate element m[i][i-1] (lower diagonal). */
if (m[i-1][1] == 0) return FALSE;
t = m[i][0] / m[i-1][1]; /* Find ratio between the two lines. */
m[i][0] = m[i][0] - m[i-1][1] * t;
m[i][1] = m[i][1] - m[i-1][2] * t;
r[i] = r[i] - r[i-1] * t;
}
/* Now do back subtitution - update the solution vector X: */
if (m[n-1][1] == 0) return FALSE;
x[n-1] = r[n-1] / m[n-1][1]; /* Find last element. */
for (i=n-2; i>=0; i--) {
if (m[i][1] == 0) return FALSE;
x[i] = (r[i] - x[i+1] * m[i][2]) / m[i][1];
}
return TRUE;
}
/*
* Generate a Bspline curve defined by all the points given in linked list p:
* Algorithm: using deBoor algorithm
* Note: if Curvekind is OPEN_CONTOUR than Open end knot vector is assumed,
* else (CLOSED_CONTOUR) Float end knot vector is assumed.
* It is assumed that num_of_points is at list 2, and order of Bspline is less
* than num_of_points!
*/
static gen_bspline_approx(p_cntr, num_of_points, order, contour_kind)
struct cntr_struct *p_cntr;
int num_of_points, order, contour_kind;
{
int i, knot_index = 0, pts_count = 1;
double dt, t, next_t, t_min, t_max, x, y;
struct cntr_struct *pc_temp = p_cntr, *pc_tail;
/* If the contour is Closed one we must update few things: */
/* 1. Make the list temporary circular, so we can close the contour. */
/* 2. Update num_of_points - increase it by "order-1" so contour will be */
/* closed. This will evaluate order more sections to close it! */
if (contour_kind == CLOSED_CONTOUR) {
pc_tail = p_cntr;
while (pc_tail -> next) pc_tail = pc_tail -> next;/* Find last point.*/
pc_tail -> next = p_cntr; /* Close contour list - make it circular.*/
num_of_points += order;
}
/* Find first (t_min) and last (t_max) t value to eval: */
t = t_min = fetch_knot(contour_kind, num_of_points, order, order);
t_max = fetch_knot(contour_kind, num_of_points, order, num_of_points);
next_t = t_min + 1.0;
knot_index = order;
dt = 1.0/num_approx_pts; /* Number of points per one section. */
while (t<t_max) {
if (t > next_t) {
pc_temp = pc_temp -> next; /* Next order ctrl. pt. to blend. */
knot_index++;
next_t += 1.0;
}
eval_bspline(t, pc_temp, num_of_points, order, knot_index,
contour_kind, &x, &y); /* Next pt. */
add_cntr_point(x, y);
pts_count++;
/* As we might have some real number round off problems we must */
/* test if we dont produce too many points here... */
if (pts_count + 1 == num_approx_pts * (num_of_points - order) + 1)
break;
t += dt;
}
eval_bspline(t_max - EPSILON, pc_temp, num_of_points, order, knot_index,
contour_kind, &x, &y);
/* If from round off errors we need more than one last point: */
for (i=pts_count; i<num_approx_pts * (num_of_points - order) + 1; i++)
add_cntr_point(x, y); /* Complete the contour. */
if (contour_kind == CLOSED_CONTOUR) /* Update list - un-circular it. */
pc_tail -> next = NULL;
}
/*
* The recursive routine to evaluate the B-spline value at point t using
* knot vector PKList, and the control points Pdtemp. Returns x, y after the
* division by the weight w. Note that Pdtemp points on the first control
* point to blend with. The B-spline is of order order.
*/
static eval_bspline(t, p_cntr, num_of_points, order, j, contour_kind, x, y)
double t;
struct cntr_struct *p_cntr;
int num_of_points, order, j, contour_kind;
double *x, *y;
{
int i, p;
double ti, tikp, *dx, *dy; /* Copy p_cntr into it to make it faster. */
dx = (double *) alloc((unsigned) (sizeof(double) * (order + j)),
"contour b_spline");
dy = (double *) alloc((unsigned) (sizeof(double) * (order + j)),
"contour b_spline");
/* Set the dx/dy - [0] iteration step, control points (p==0 iterat.): */
for (i=j-order; i<=j; i++) {
dx[i] = p_cntr -> X;
dy[i] = p_cntr -> Y;
p_cntr = p_cntr -> next;
}
for (p=1; p<=order; p++) { /* Iteration (b-spline level) counter. */
for (i=j; i>=j-order+p; i--) { /* Control points indexing. */
ti = fetch_knot(contour_kind, num_of_points, order, i);
tikp = fetch_knot(contour_kind, num_of_points, order, i+order+1-p);
if (ti == tikp) { /* Should not be a problems but how knows... */
}
else {
dx[i] = dx[i] * (t - ti)/(tikp-ti) + /* Calculate x. */
dx[i-1] * (tikp-t)/(tikp-ti);
dy[i] = dy[i] * (t - ti)/(tikp-ti) + /* Calculate y. */
dy[i-1] * (tikp-t)/(tikp-ti);
}
}
}
*x = dx[j]; *y = dy[j];
free((char *) dx);
free((char *) dy);
}
/*
* Routine to get the i knot from uniform knot vector. The knot vector
* might be float (Knot(i) = i) or open (where the first and last "order"
* knots are equal). contour_kind determines knot kind - OPEN_CONTOUR means
* open knot vector, and CLOSED_CONTOUR selects float knot vector.
* Note the knot vector is not exist and this routine simulates it existance
* Also note the indexes for the knot vector starts from 0.
*/
static double fetch_knot(contour_kind, num_of_points, order, i)
int contour_kind, num_of_points, order, i;
{
switch (contour_kind) {
case OPEN_CONTOUR:
if (i <= order) return 0.0;
else if (i <= num_of_points) return (double) (i - order);
else return (double) (num_of_points - order);
case CLOSED_CONTOUR:
return (double) i;
default: /* Should never happen */
return 1.0;
}
}