/src/PROJ/src/projections/imoll_o.cpp

Source


#include <errno.h>
#include <math.h>

#include "proj.h"
#include "proj_internal.h"

PROJ_HEAD(imoll_o, "Interrupted Mollweide Oceanic View") "\n\tPCyl, Sph";

/*
This projection is a variant of the Interrupted Mollweide projection
that emphasizes ocean areas.
This projection is a compilation of 6 separate sub-projections.
It is related to the Interrupted Goode Homolosine projection,
but uses Mollweide at all latitudes.

Each sub-projection is assigned an integer label
numbered 1 through 6. Most of this code contains logic to assign
the labels based on latitude (phi) and longitude (lam) regions.
The code is adapted from igh.cpp.

Original Reference:
J. Paul Goode (1919) STUDIES IN PROJECTIONS: ADAPTING THE
    HOMOLOGRAPHIC PROJECTION TO THE PORTRAYAL OF THE EARTH'S
    ENTIRE SURFACE, Bul. Geog. SOC.Phila., Vol. XWIJNO.3.
    July, 1919, pp. 103-113.
*/

C_NAMESPACE PJ *pj_moll(PJ *);

namespace pj_imoll_o_ns {
struct pj_imoll_o_data {
    struct PJconsts *pj[6];
    // We need to know the inverse boundary locations of the "seams".
    double boundary12;
    double boundary23;
    double boundary45;
    double boundary56;
};

/* SIMPLIFY THIS */
constexpr double d10 = 10 * DEG_TO_RAD;
constexpr double d20 = 20 * DEG_TO_RAD;
constexpr double d60 = 60 * DEG_TO_RAD;
constexpr double d90 = 90 * DEG_TO_RAD;
constexpr double d110 = 110 * DEG_TO_RAD;
constexpr double d130 = 130 * DEG_TO_RAD;
constexpr double d140 = 140 * DEG_TO_RAD;
constexpr double d150 = 150 * DEG_TO_RAD;
constexpr double d180 = 180 * DEG_TO_RAD;

constexpr double EPSLN =
    1.e-10; /* allow a little 'slack' on zone edge positions */

} // namespace pj_imoll_o_ns

/*
Assign an integer index representing each of the 6
sub-projection zones based on latitude (phi) and
longitude (lam) ranges.
*/

static PJ_XY imoll_o_s_forward(PJ_LP lp, PJ *P) { /* Spheroidal, forward */
    using namespace pj_imoll_o_ns;

    PJ_XY xy;
    struct pj_imoll_o_data *Q =
        static_cast<struct pj_imoll_o_data *>(P->opaque);
    int z;

    if (lp.phi >= 0) { /* 1|2|3 */
        if (lp.lam <= -d90)
            z = 1;
        else if (lp.lam >= d60)
            z = 3;
        else
            z = 2;
    } else {
        if (lp.lam <= -d60)
            z = 4;
        else if (lp.lam >= d90)
            z = 6;
        else
            z = 5;
    }

    lp.lam -= Q->pj[z - 1]->lam0;
    xy = Q->pj[z - 1]->fwd(lp, Q->pj[z - 1]);
    xy.x += Q->pj[z - 1]->x0;
    xy.y += Q->pj[z - 1]->y0;

    return xy;
}

static PJ_LP imoll_o_s_inverse(PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
    using namespace pj_imoll_o_ns;

    PJ_LP lp = {0.0, 0.0};
    struct pj_imoll_o_data *Q =
        static_cast<struct pj_imoll_o_data *>(P->opaque);
    const double y90 = sqrt(2.0); /* lt=90 corresponds to y=sqrt(2) */

    int z = 0;
    if (xy.y > y90 + EPSLN || xy.y < -y90 + EPSLN) /* 0 */
        z = 0;
    else if (xy.y >= 0) {
        if (xy.x <= Q->boundary12)
            z = 1;
        else if (xy.x >= Q->boundary23)
            z = 3;
        else
            z = 2;
    } else {
        if (xy.x <= Q->boundary45)
            z = 4;
        else if (xy.x >= Q->boundary56)
            z = 6;
        else
            z = 5;
    }

    if (z) {
        bool ok = false;

        xy.x -= Q->pj[z - 1]->x0;
        xy.y -= Q->pj[z - 1]->y0;
        lp = Q->pj[z - 1]->inv(xy, Q->pj[z - 1]);
        lp.lam += Q->pj[z - 1]->lam0;

        switch (z) {
        case 1:
            ok = ((lp.lam >= -d180 - EPSLN && lp.lam <= -d90 + EPSLN) &&
                  (lp.phi >= 0.0 - EPSLN));
            break;
        case 2:
            ok = ((lp.lam >= -d90 - EPSLN && lp.lam <= d60 + EPSLN) &&
                  (lp.phi >= 0.0 - EPSLN));
            break;
        case 3:
            ok = ((lp.lam >= d60 - EPSLN && lp.lam <= d180 + EPSLN) &&
                  (lp.phi >= 0.0 - EPSLN));
            break;
        case 4:
            ok = ((lp.lam >= -d180 - EPSLN && lp.lam <= -d60 + EPSLN) &&
                  (lp.phi <= 0.0 + EPSLN));
            break;
        case 5:
            ok = ((lp.lam >= -d60 - EPSLN && lp.lam <= d90 + EPSLN) &&
                  (lp.phi <= 0.0 + EPSLN));
            break;
        case 6:
            ok = ((lp.lam >= d90 - EPSLN && lp.lam <= d180 + EPSLN) &&
                  (lp.phi <= 0.0 + EPSLN));
            break;
        }
        z = (!ok ? 0 : z); /* projectable? */
    }

    if (!z)
        lp.lam = HUGE_VAL;
    if (!z)
        lp.phi = HUGE_VAL;

    return lp;
}

static PJ *pj_imoll_o_destructor(PJ *P, int errlev) {
    using namespace pj_imoll_o_ns;

    int i;
    if (nullptr == P)
        return nullptr;

    if (nullptr == P->opaque)
        return pj_default_destructor(P, errlev);

    struct pj_imoll_o_data *Q =
        static_cast<struct pj_imoll_o_data *>(P->opaque);

    for (i = 0; i < 6; ++i) {
        if (Q->pj[i])
            Q->pj[i]->destructor(Q->pj[i], errlev);
    }

    return pj_default_destructor(P, errlev);
}

/*
  Zones:

    -180       -90               60           180
      +---------+----------------+-------------+
      |1        |2               |3            |
      |         |                |             |
      |         |                |             |
      |         |                |             |
      |         |                |             |
    0 +---------+--+-------------+--+----------+
      |4           |5               |6         |
      |            |                |          |
      |            |                |          |
      |            |                |          |
      |            |                |          |
      +------------+----------------+----------+
    -180          -60               90        180
*/

static bool pj_imoll_o_setup_zone(PJ *P,
                                  struct pj_imoll_o_ns::pj_imoll_o_data *Q,
                                  int n, PJ *(*proj_ptr)(PJ *), double x_0,
                                  double y_0, double lon_0) {
    if (!(Q->pj[n - 1] = proj_ptr(nullptr)))
        return false;
    if (!(Q->pj[n - 1] = proj_ptr(Q->pj[n - 1])))
        return false;
    Q->pj[n - 1]->ctx = P->ctx;
    Q->pj[n - 1]->x0 = x_0;
    Q->pj[n - 1]->y0 = y_0;
    Q->pj[n - 1]->lam0 = lon_0;
    return true;
}

static double
pj_imoll_o_compute_zone_offset(struct pj_imoll_o_ns::pj_imoll_o_data *Q,
                               int zone1, int zone2, double lam, double phi1,
                               double phi2) {
    PJ_LP lp1, lp2;
    PJ_XY xy1, xy2;

    lp1.lam = lam - (Q->pj[zone1 - 1]->lam0);
    lp1.phi = phi1;
    lp2.lam = lam - (Q->pj[zone2 - 1]->lam0);
    lp2.phi = phi2;
    xy1 = Q->pj[zone1 - 1]->fwd(lp1, Q->pj[zone1 - 1]);
    xy2 = Q->pj[zone2 - 1]->fwd(lp2, Q->pj[zone2 - 1]);
    return (xy2.x + Q->pj[zone2 - 1]->x0) - (xy1.x + Q->pj[zone1 - 1]->x0);
}

static double pj_imoll_o_compute_zone_x_boundary(PJ *P, double lam,
                                                 double phi) {
    PJ_LP lp1, lp2;
    PJ_XY xy1, xy2;

    lp1.lam = lam - pj_imoll_o_ns::EPSLN;
    lp1.phi = phi;
    lp2.lam = lam + pj_imoll_o_ns::EPSLN;
    lp2.phi = phi;
    xy1 = imoll_o_s_forward(lp1, P);
    xy2 = imoll_o_s_forward(lp2, P);
    return (xy1.x + xy2.x) / 2.;
}

PJ *PJ_PROJECTION(imoll_o) {
    using namespace pj_imoll_o_ns;

    struct pj_imoll_o_data *Q = static_cast<struct pj_imoll_o_data *>(
        calloc(1, sizeof(struct pj_imoll_o_data)));
    if (nullptr == Q)
        return pj_default_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/);
    P->opaque = Q;

    /* Setup zones */
    if (!pj_imoll_o_setup_zone(P, Q, 1, pj_moll, -d140, 0, -d140) ||
        !pj_imoll_o_setup_zone(P, Q, 2, pj_moll, -d10, 0, -d10) ||
        !pj_imoll_o_setup_zone(P, Q, 3, pj_moll, d130, 0, d130) ||
        !pj_imoll_o_setup_zone(P, Q, 4, pj_moll, -d110, 0, -d110) ||
        !pj_imoll_o_setup_zone(P, Q, 5, pj_moll, d20, 0, d20) ||
        !pj_imoll_o_setup_zone(P, Q, 6, pj_moll, d150, 0, d150)) {
        return pj_imoll_o_destructor(P, PROJ_ERR_OTHER /*ENOMEM*/);
    }

    /* Adjust zones */

    /* Match 2 (center) to 1 (west) */
    Q->pj[1]->x0 +=
        pj_imoll_o_compute_zone_offset(Q, 2, 1, -d90, 0.0 + EPSLN, 0.0 + EPSLN);

    /* Match 3 (east) to 2 (center) */
    Q->pj[2]->x0 +=
        pj_imoll_o_compute_zone_offset(Q, 3, 2, d60, 0.0 + EPSLN, 0.0 + EPSLN);

    /* Match 4 (south) to 1 (north) */
    Q->pj[3]->x0 += pj_imoll_o_compute_zone_offset(Q, 4, 1, -d180, 0.0 - EPSLN,
                                                   0.0 + EPSLN);

    /* Match 5 (south) to 2 (north) */
    Q->pj[4]->x0 +=
        pj_imoll_o_compute_zone_offset(Q, 5, 2, -d60, 0.0 - EPSLN, 0.0 + EPSLN);

    /* Match 6 (south) to 3 (north) */
    Q->pj[5]->x0 +=
        pj_imoll_o_compute_zone_offset(Q, 6, 3, d90, 0.0 - EPSLN, 0.0 + EPSLN);

    /*
      The most straightforward way of computing the x locations of the "seams"
      in the interrupted projection is to compute the forward transform at the
      seams and record these values.
    */
    Q->boundary12 = pj_imoll_o_compute_zone_x_boundary(P, -d90, 0.0 + EPSLN);
    Q->boundary23 = pj_imoll_o_compute_zone_x_boundary(P, d60, 0.0 + EPSLN);
    Q->boundary45 = pj_imoll_o_compute_zone_x_boundary(P, -d60, 0.0 - EPSLN);
    Q->boundary56 = pj_imoll_o_compute_zone_x_boundary(P, d90, 0.0 - EPSLN);

    P->inv = imoll_o_s_inverse;
    P->fwd = imoll_o_s_forward;
    P->destructor = pj_imoll_o_destructor;
    P->es = 0.;

    return P;
}

Coverage Report

Created: 2026-03-22 06:35

Line	Count	Source
1
2
3		#include <errno.h>
4		#include <math.h>
5
6		#include "proj.h"
7		#include "proj_internal.h"
8
9		PROJ_HEAD(imoll_o, "Interrupted Mollweide Oceanic View") "\n\tPCyl, Sph";
10
11		/*
12		This projection is a variant of the Interrupted Mollweide projection
13		that emphasizes ocean areas.
14		This projection is a compilation of 6 separate sub-projections.
15		It is related to the Interrupted Goode Homolosine projection,
16		but uses Mollweide at all latitudes.
17
18		Each sub-projection is assigned an integer label
19		numbered 1 through 6. Most of this code contains logic to assign
20		the labels based on latitude (phi) and longitude (lam) regions.
21		The code is adapted from igh.cpp.
22
23		Original Reference:
24		J. Paul Goode (1919) STUDIES IN PROJECTIONS: ADAPTING THE
25		HOMOLOGRAPHIC PROJECTION TO THE PORTRAYAL OF THE EARTH'S
26		ENTIRE SURFACE, Bul. Geog. SOC.Phila., Vol. XWIJNO.3.
27		July, 1919, pp. 103-113.
28		*/
29
30		C_NAMESPACE PJ pj_moll(PJ );
31
32		namespace pj_imoll_o_ns {
33		struct pj_imoll_o_data {
34		struct PJconsts *pj[6];
35		// We need to know the inverse boundary locations of the "seams".
36		double boundary12;
37		double boundary23;
38		double boundary45;
39		double boundary56;
40		};
41
42		/* SIMPLIFY THIS */
43		constexpr double d10 = 10 * DEG_TO_RAD;
44		constexpr double d20 = 20 * DEG_TO_RAD;
45		constexpr double d60 = 60 * DEG_TO_RAD;
46		constexpr double d90 = 90 * DEG_TO_RAD;
47		constexpr double d110 = 110 * DEG_TO_RAD;
48		constexpr double d130 = 130 * DEG_TO_RAD;
49		constexpr double d140 = 140 * DEG_TO_RAD;
50		constexpr double d150 = 150 * DEG_TO_RAD;
51		constexpr double d180 = 180 * DEG_TO_RAD;
52
53		constexpr double EPSLN =
54		1.e-10; /* allow a little 'slack' on zone edge positions */
55
56		} // namespace pj_imoll_o_ns
57
58		/*
59		Assign an integer index representing each of the 6
60		sub-projection zones based on latitude (phi) and
61		longitude (lam) ranges.
62		*/
63
64	24	static PJ_XY imoll_o_s_forward(PJ_LP lp, PJ P) { / Spheroidal, forward */
65	24	using namespace pj_imoll_o_ns;
66
67	24	PJ_XY xy;
68	24	struct pj_imoll_o_data *Q =
69	24	static_cast<struct pj_imoll_o_data *>(P->opaque);
70	24	int z;
71
72	24	if (lp.phi >= 0) { /* 1\|2\|3 */
73	12	if (lp.lam <= -d90)
74	3	z = 1;
75	9	else if (lp.lam >= d60)
76	3	z = 3;
77	6	else
78	6	z = 2;
79	12	} else {
80	12	if (lp.lam <= -d60)
81	3	z = 4;
82	9	else if (lp.lam >= d90)
83	3	z = 6;
84	6	else
85	6	z = 5;
86	12	}
87
88	24	lp.lam -= Q->pj[z - 1]->lam0;
89	24	xy = Q->pj[z - 1]->fwd(lp, Q->pj[z - 1]);
90	24	xy.x += Q->pj[z - 1]->x0;
91	24	xy.y += Q->pj[z - 1]->y0;
92
93	24	return xy;
94	24	}
95
96	0	static PJ_LP imoll_o_s_inverse(PJ_XY xy, PJ P) { / Spheroidal, inverse */
97	0	using namespace pj_imoll_o_ns;
98
99	0	PJ_LP lp = {0.0, 0.0};
100	0	struct pj_imoll_o_data *Q =
101	0	static_cast<struct pj_imoll_o_data *>(P->opaque);
102	0	const double y90 = sqrt(2.0); /* lt=90 corresponds to y=sqrt(2) */
103
104	0	int z = 0;
105	0	if (xy.y > y90 + EPSLN \|\| xy.y < -y90 + EPSLN) /* 0 */
106	0	z = 0;
107	0	else if (xy.y >= 0) {
108	0	if (xy.x <= Q->boundary12)
109	0	z = 1;
110	0	else if (xy.x >= Q->boundary23)
111	0	z = 3;
112	0	else
113	0	z = 2;
114	0	} else {
115	0	if (xy.x <= Q->boundary45)
116	0	z = 4;
117	0	else if (xy.x >= Q->boundary56)
118	0	z = 6;
119	0	else
120	0	z = 5;
121	0	}
122
123	0	if (z) {
124	0	bool ok = false;
125
126	0	xy.x -= Q->pj[z - 1]->x0;
127	0	xy.y -= Q->pj[z - 1]->y0;
128	0	lp = Q->pj[z - 1]->inv(xy, Q->pj[z - 1]);
129	0	lp.lam += Q->pj[z - 1]->lam0;
130
131	0	switch (z) {
132	0	case 1:
133	0	ok = ((lp.lam >= -d180 - EPSLN && lp.lam <= -d90 + EPSLN) &&
134	0	(lp.phi >= 0.0 - EPSLN));
135	0	break;
136	0	case 2:
137	0	ok = ((lp.lam >= -d90 - EPSLN && lp.lam <= d60 + EPSLN) &&
138	0	(lp.phi >= 0.0 - EPSLN));
139	0	break;
140	0	case 3:
141	0	ok = ((lp.lam >= d60 - EPSLN && lp.lam <= d180 + EPSLN) &&
142	0	(lp.phi >= 0.0 - EPSLN));
143	0	break;
144	0	case 4:
145	0	ok = ((lp.lam >= -d180 - EPSLN && lp.lam <= -d60 + EPSLN) &&
146	0	(lp.phi <= 0.0 + EPSLN));
147	0	break;
148	0	case 5:
149	0	ok = ((lp.lam >= -d60 - EPSLN && lp.lam <= d90 + EPSLN) &&
150	0	(lp.phi <= 0.0 + EPSLN));
151	0	break;
152	0	case 6:
153	0	ok = ((lp.lam >= d90 - EPSLN && lp.lam <= d180 + EPSLN) &&
154	0	(lp.phi <= 0.0 + EPSLN));
155	0	break;
156	0	}
157	0	z = (!ok ? 0 : z); /* projectable? */
158	0	}
159
160	0	if (!z)
161	0	lp.lam = HUGE_VAL;
162	0	if (!z)
163	0	lp.phi = HUGE_VAL;
164
165	0	return lp;
166	0	}
167
168	3	static PJ pj_imoll_o_destructor(PJ P, int errlev) {
169	3	using namespace pj_imoll_o_ns;
170
171	3	int i;
172	3	if (nullptr == P)
173	0	return nullptr;
174
175	3	if (nullptr == P->opaque)
176	0	return pj_default_destructor(P, errlev);
177
178	3	struct pj_imoll_o_data *Q =
179	3	static_cast<struct pj_imoll_o_data *>(P->opaque);
180
181	21	for (i = 0; i < 6; ++i) {
182	18	if (Q->pj[i])
183	18	Q->pj[i]->destructor(Q->pj[i], errlev);
184	18	}
185
186	3	return pj_default_destructor(P, errlev);
187	3	}
188
189		/*
190		Zones:
191
192		-180 -90 60 180
193		+---------+----------------+-------------+
194		\|1 \|2 \|3 \|
195		\| \| \| \|
196		\| \| \| \|
197		\| \| \| \|
198		\| \| \| \|
199		0 +---------+--+-------------+--+----------+
200		\|4 \|5 \|6 \|
201		\| \| \| \|
202		\| \| \| \|
203		\| \| \| \|
204		\| \| \| \|
205		+------------+----------------+----------+
206		-180 -60 90 180
207		*/
208
209		static bool pj_imoll_o_setup_zone(PJ *P,
210		struct pj_imoll_o_ns::pj_imoll_o_data *Q,
211		int n, PJ (proj_ptr)(PJ *), double x_0,
212	18	double y_0, double lon_0) {
213	18	if (!(Q->pj[n - 1] = proj_ptr(nullptr)))
214	0	return false;
215	18	if (!(Q->pj[n - 1] = proj_ptr(Q->pj[n - 1])))
216	0	return false;
217	18	Q->pj[n - 1]->ctx = P->ctx;
218	18	Q->pj[n - 1]->x0 = x_0;
219	18	Q->pj[n - 1]->y0 = y_0;
220	18	Q->pj[n - 1]->lam0 = lon_0;
221	18	return true;
222	18	}
223
224		static double
225		pj_imoll_o_compute_zone_offset(struct pj_imoll_o_ns::pj_imoll_o_data *Q,
226		int zone1, int zone2, double lam, double phi1,
227	15	double phi2) {
228	15	PJ_LP lp1, lp2;
229	15	PJ_XY xy1, xy2;
230
231	15	lp1.lam = lam - (Q->pj[zone1 - 1]->lam0);
232	15	lp1.phi = phi1;
233	15	lp2.lam = lam - (Q->pj[zone2 - 1]->lam0);
234	15	lp2.phi = phi2;
235	15	xy1 = Q->pj[zone1 - 1]->fwd(lp1, Q->pj[zone1 - 1]);
236	15	xy2 = Q->pj[zone2 - 1]->fwd(lp2, Q->pj[zone2 - 1]);
237	15	return (xy2.x + Q->pj[zone2 - 1]->x0) - (xy1.x + Q->pj[zone1 - 1]->x0);
238	15	}
239
240		static double pj_imoll_o_compute_zone_x_boundary(PJ *P, double lam,
241	12	double phi) {
242	12	PJ_LP lp1, lp2;
243	12	PJ_XY xy1, xy2;
244
245	12	lp1.lam = lam - pj_imoll_o_ns::EPSLN;
246	12	lp1.phi = phi;
247	12	lp2.lam = lam + pj_imoll_o_ns::EPSLN;
248	12	lp2.phi = phi;
249	12	xy1 = imoll_o_s_forward(lp1, P);
250	12	xy2 = imoll_o_s_forward(lp2, P);
251	12	return (xy1.x + xy2.x) / 2.;
252	12	}
253
254	3	PJ *PJ_PROJECTION(imoll_o) {
255	3	using namespace pj_imoll_o_ns;
256
257	3	struct pj_imoll_o_data Q = static_cast<struct pj_imoll_o_data >(
258	3	calloc(1, sizeof(struct pj_imoll_o_data)));
259	3	if (nullptr == Q)
260	0	return pj_default_destructor(P, PROJ_ERR_OTHER /ENOMEM/);
261	3	P->opaque = Q;
262
263		/* Setup zones */
264	3	if (!pj_imoll_o_setup_zone(P, Q, 1, pj_moll, -d140, 0, -d140) \|\|
265	3	!pj_imoll_o_setup_zone(P, Q, 2, pj_moll, -d10, 0, -d10) \|\|
266	3	!pj_imoll_o_setup_zone(P, Q, 3, pj_moll, d130, 0, d130) \|\|
267	3	!pj_imoll_o_setup_zone(P, Q, 4, pj_moll, -d110, 0, -d110) \|\|
268	3	!pj_imoll_o_setup_zone(P, Q, 5, pj_moll, d20, 0, d20) \|\|
269	3	!pj_imoll_o_setup_zone(P, Q, 6, pj_moll, d150, 0, d150)) {
270	0	return pj_imoll_o_destructor(P, PROJ_ERR_OTHER /ENOMEM/);
271	0	}
272
273		/* Adjust zones */
274
275		/* Match 2 (center) to 1 (west) */
276	3	Q->pj[1]->x0 +=
277	3	pj_imoll_o_compute_zone_offset(Q, 2, 1, -d90, 0.0 + EPSLN, 0.0 + EPSLN);
278
279		/* Match 3 (east) to 2 (center) */
280	3	Q->pj[2]->x0 +=
281	3	pj_imoll_o_compute_zone_offset(Q, 3, 2, d60, 0.0 + EPSLN, 0.0 + EPSLN);
282
283		/* Match 4 (south) to 1 (north) */
284	3	Q->pj[3]->x0 += pj_imoll_o_compute_zone_offset(Q, 4, 1, -d180, 0.0 - EPSLN,
285	3	0.0 + EPSLN);
286
287		/* Match 5 (south) to 2 (north) */
288	3	Q->pj[4]->x0 +=
289	3	pj_imoll_o_compute_zone_offset(Q, 5, 2, -d60, 0.0 - EPSLN, 0.0 + EPSLN);
290
291		/* Match 6 (south) to 3 (north) */
292	3	Q->pj[5]->x0 +=
293	3	pj_imoll_o_compute_zone_offset(Q, 6, 3, d90, 0.0 - EPSLN, 0.0 + EPSLN);
294
295		/*
296		The most straightforward way of computing the x locations of the "seams"
297		in the interrupted projection is to compute the forward transform at the
298		seams and record these values.
299		*/
300	3	Q->boundary12 = pj_imoll_o_compute_zone_x_boundary(P, -d90, 0.0 + EPSLN);
301	3	Q->boundary23 = pj_imoll_o_compute_zone_x_boundary(P, d60, 0.0 + EPSLN);
302	3	Q->boundary45 = pj_imoll_o_compute_zone_x_boundary(P, -d60, 0.0 - EPSLN);
303	3	Q->boundary56 = pj_imoll_o_compute_zone_x_boundary(P, d90, 0.0 - EPSLN);
304
305	3	P->inv = imoll_o_s_inverse;
306	3	P->fwd = imoll_o_s_forward;
307	3	P->destructor = pj_imoll_o_destructor;
308	3	P->es = 0.;
309
310	3	return P;
311	3	}