TEAPOT TIME!

4 files changed, 486 insertions, 4 deletions

diff --git a/README.md b/README.md
index 6012a9f..1886dba 100644
--- a/README.md
+++ b/README.md
@@ -55,9 +55,9 @@ context. See examples for usage.
 cc -Iinclude your_app.c lib/libGL.a -lm -o your_app
 ```
 
-The `examples/` (`cube`, `rave`) contain runnable programs. Buidl and run
-as the user with permissions to `/dev/verite3d`, point `VERITE_UCODE` 
-evironment variable at the `v2000gl.uc` 3D microcode.
+The `examples/` contain runnable programs. Build
+and run as the user with permissions to `/dev/verite3d`, point `VERITE_UCODE`
+environment variable at the `v2000gl.uc` 3D microcode.
 
 If the `/dev/verite3d` does not exist on your system, despite running a
 kernel with `veritefb(4)` driver loaded, create it using `MAKEDEV`.
diff --git a/examples/Makefile b/examples/Makefile
index c2d2176..ee05725 100644
--- a/examples/Makefile
+++ b/examples/Makefile
@@ -7,7 +7,7 @@ GLINC    = -I$(TOP)/include
 LIBGL    = $(TOP)/lib/libGL.a
 LIBS     = -lm
 
-PROGS    = cube rave
+PROGS    = cube rave teapot
 
 .PHONY: all clean
 all: $(PROGS)
@@ -15,6 +15,8 @@ all: $(PROGS)
 $(PROGS): %: %.c $(LIBGL)
 	$(CC) $(CFLAGS) $(GLINC) $< $(LIBGL) $(LIBS) -o $@
 
+teapot: teapot_data.inc
+
 clean:
 	rm -f $(PROGS)
 
diff --git a/examples/teapot.c b/examples/teapot.c
new file mode 100644
index 0000000..ff67f95
--- /dev/null
+++ b/examples/teapot.c
@@ -0,0 +1,288 @@
+/*
+ * teapot - the Utah teapot, lit and spinning
+ *
+ * Build:
+ *   cc -O2 -I../include -o teapot teapot.c ../lib/libGL.a -lm
+ *
+ * Run: VERITE_UCODE=$HOME/v2000gl.uc \
+ *             ./teapot [seconds]   (0 = spin until ^C)
+ *
+ * Tessellation density is TEAPOT_GRID (default 8)...
+ */
+#include <sys/time.h>
+#include <math.h>
+#include <signal.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#include <GL/gl.h>
+#include <GL/vrmesa.h>
+
+static const GLfloat teapot_patch[32][4][4][3] = {
+#include "teapot_data.inc"
+};
+
+static volatile sig_atomic_t stop;
+
+static void
+onint(int sig)
+{
+
+	(void)sig;
+	stop = 1;
+}
+
+/* Cubic Bernstein basis and its derivative at t. */
+static void
+bernstein(float t, float b[4], float db[4])
+{
+	float it = 1.0f - t;
+
+	b[0] = it * it * it;
+	b[1] = 3.0f * t * it * it;
+	b[2] = 3.0f * t * t * it;
+	b[3] = t * t * t;
+
+	db[0] = -3.0f * it * it;
+	db[1] = 3.0f * it * it - 6.0f * t * it;
+	db[2] = 6.0f * t * it - 3.0f * t * t;
+	db[3] = 3.0f * t * t;
+}
+
+/*
+ * Evaluate patch p at (u,v)
+ */
+static void
+eval_patch(int p, float u, float v, float pos[3], float nrm[3])
+{
+	float bu[4], dbu[4], bv[4], dbv[4];
+	float du[3], dv[3], len;
+	int i, j, k;
+
+	if (u < 1e-4f)
+		u = 1e-4f;
+	else if (u > 1.0f - 1e-4f)
+		u = 1.0f - 1e-4f;
+	if (v < 1e-4f)
+		v = 1e-4f;
+	else if (v > 1.0f - 1e-4f)
+		v = 1.0f - 1e-4f;
+
+	bernstein(u, bu, dbu);
+	bernstein(v, bv, dbv);
+
+	for (k = 0; k < 3; k++)
+		pos[k] = du[k] = dv[k] = 0.0f;
+
+	for (i = 0; i < 4; i++)
+		for (j = 0; j < 4; j++) {
+			const GLfloat *cp = teapot_patch[p][i][j];
+			float w  = bu[i] * bv[j];
+			float wu = dbu[i] * bv[j];
+			float wv = bu[i] * dbv[j];
+
+			for (k = 0; k < 3; k++) {
+				pos[k] += w  * cp[k];
+				du[k]  += wu * cp[k];
+				dv[k]  += wv * cp[k];
+			}
+		}
+
+	/* normal = du x dv (points outward across the whole teaset) */
+	nrm[0] = du[1] * dv[2] - du[2] * dv[1];
+	nrm[1] = du[2] * dv[0] - du[0] * dv[2];
+	nrm[2] = du[0] * dv[1] - du[1] * dv[0];
+	len = sqrtf(nrm[0] * nrm[0] + nrm[1] * nrm[1] + nrm[2] * nrm[2]);
+	if (len > 1e-8f) {
+		nrm[0] /= len;
+		nrm[1] /= len;
+		nrm[2] /= len;
+	} else {
+		nrm[0] = nrm[1] = 0.0f;
+		nrm[2] = 1.0f;
+	}
+}
+
+struct vtx {
+	GLfloat p[3];
+	GLfloat n[3];
+};
+
+static int		grid;		/* steps per patch edge */
+static int		row;		/* vertices per patch edge = grid + 1 */
+static struct vtx	*mesh;		/* [32][row*row], contiguous */
+
+static void
+build_mesh(void)
+{
+	GLfloat lo[3], hi[3];
+	GLfloat cx, cy, cz, dim, m, gscale;
+	int p, a, b, k, n, nverts;
+
+	row = grid + 1;
+	nverts = 32 * row * row;
+	mesh = malloc((size_t)nverts * sizeof(*mesh));
+	if (mesh == NULL) {
+		perror("malloc");
+		exit(1);
+	}
+
+	for (k = 0; k < 3; k++) {
+		lo[k] = 1e30f;
+		hi[k] = -1e30f;
+	}
+
+	for (p = 0; p < 32; p++)
+		for (a = 0; a < row; a++)
+			for (b = 0; b < row; b++) {
+				struct vtx *vp = &mesh[(p * row + a) * row + b];
+
+				eval_patch(p, (float)a / grid, (float)b / grid,
+				    vp->p, vp->n);
+				for (k = 0; k < 3; k++) {
+					if (vp->p[k] < lo[k])
+						lo[k] = vp->p[k];
+					if (vp->p[k] > hi[k])
+						hi[k] = vp->p[k];
+				}
+			}
+
+	/* Bake centre + uniform scale into the vertices so the modelview needs
+	 * no scale and the unit normals need no GL_NORMALIZE. */
+	cx = 0.5f * (lo[0] + hi[0]);
+	cy = 0.5f * (lo[1] + hi[1]);
+	cz = 0.5f * (lo[2] + hi[2]);
+	dim = hi[0] - lo[0];
+	m = hi[1] - lo[1];
+	if (m > dim)
+		dim = m;
+	m = hi[2] - lo[2];
+	if (m > dim)
+		dim = m;
+	gscale = 3.0f / dim;
+	for (n = 0; n < nverts; n++) {
+		mesh[n].p[0] = (mesh[n].p[0] - cx) * gscale;
+		mesh[n].p[1] = (mesh[n].p[1] - cy) * gscale;
+		mesh[n].p[2] = (mesh[n].p[2] - cz) * gscale;
+	}
+}
+
+static void
+draw_teapot(void)
+{
+	int p, a, b;
+
+	for (p = 0; p < 32; p++)
+		for (a = 0; a < grid; a++) {
+			const struct vtx *r0 = &mesh[(p * row + a) * row];
+			const struct vtx *r1 = &mesh[(p * row + a + 1) * row];
+
+			glBegin(GL_TRIANGLE_STRIP);
+			for (b = 0; b < row; b++) {
+				glNormal3fv(r0[b].n);
+				glVertex3fv(r0[b].p);
+				glNormal3fv(r1[b].n);
+				glVertex3fv(r1[b].p);
+			}
+			glEnd();
+		}
+}
+
+int
+main(int argc, char **argv)
+{
+	static const GLfloat lightpos[4]  = { -0.4f, 0.7f, 1.0f, 0.0f };
+	static const GLfloat lightamb[4]  = { 0.15f, 0.15f, 0.18f, 1.0f };
+	static const GLfloat lightdif[4]  = { 0.9f, 0.9f, 0.85f, 1.0f };
+	static const GLfloat lightspc[4]  = { 1.0f, 1.0f, 1.0f, 1.0f };
+	static const GLfloat matdif[4]    = { 0.75f, 0.42f, 0.16f, 1.0f };
+	static const GLfloat matspc[4]    = { 0.85f, 0.85f, 0.75f, 1.0f };
+	static const GLfloat matamb[4]    = { 0.25f, 0.14f, 0.06f, 1.0f };
+	vrMesaContext ctx;
+	struct timeval t0, t1, tstart;
+	const char *genv = getenv("TEAPOT_GRID");
+	double secs = 30.0;
+	float spin = 0.0f;
+	int frame = 0;
+
+	if (argc > 1)
+		secs = atof(argv[1]);
+	grid = genv != NULL ? atoi(genv) : 8;
+	if (grid < 2)
+		grid = 2;
+	else if (grid > 40)
+		grid = 40;
+	signal(SIGINT, onint);
+
+	build_mesh();
+
+	ctx = vrMesaCreateContext(NULL);
+	if (ctx == NULL)
+		return 1;
+	vrMesaMakeCurrent(ctx);
+	printf("GL_RENDERER: %s (%s)\n", glGetString(GL_RENDERER),
+	    glGetString(GL_VERSION));
+	printf("teapot: 32 patches, grid %d -> %d triangles\n",
+	    grid, 32 * grid * grid * 2);
+
+	glEnable(GL_DEPTH_TEST);
+	glShadeModel(GL_SMOOTH);
+	/* cross(du,dv) points outward across the whole teaset, so single-sided
+	 * lighting shades the exterior correctly and stays on the hardware
+	 * triangle path (two-sided lighting would force a swrast fallback).
+	 * Back faces fall behind the depth buffer, so culling is unnecessary. */
+	glEnable(GL_LIGHTING);
+	glEnable(GL_LIGHT0);
+	glLightfv(GL_LIGHT0, GL_AMBIENT, lightamb);
+	glLightfv(GL_LIGHT0, GL_DIFFUSE, lightdif);
+	glLightfv(GL_LIGHT0, GL_SPECULAR, lightspc);
+	glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT, matamb);
+	glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, matdif);
+	glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, matspc);
+	glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 32.0f);
+
+	glClearColor(0.07f, 0.08f, 0.11f, 1.0f);
+	glViewport(0, 0, 640, 480);
+	glMatrixMode(GL_PROJECTION);
+	glLoadIdentity();
+	glFrustum(-1.0, 1.0, -0.75, 0.75, 2.0, 80.0);
+
+	gettimeofday(&tstart, NULL);
+	t0 = tstart;
+	while (!stop) {
+		glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
+		glMatrixMode(GL_MODELVIEW);
+		glLoadIdentity();
+		glTranslatef(0.0f, -0.3f, -7.0f);
+		/* Fixed light, pinned in eye space before any model rotation. */
+		glLightfv(GL_LIGHT0, GL_POSITION, lightpos);
+		/* Stand the Z-up model upright (-90) and look slightly down (+15). */
+		glRotatef(-75.0f, 1.0f, 0.0f, 0.0f);
+		glRotatef(spin, 0.0f, 0.0f, 1.0f);	/* spin about the model axis */
+
+		draw_teapot();
+
+		vrMesaSwapBuffers();
+		spin += 1.3f;
+		if (++frame % 100 == 0) {
+			double dt;
+
+			gettimeofday(&t1, NULL);
+			dt = (t1.tv_sec - t0.tv_sec) +
+			    (t1.tv_usec - t0.tv_usec) / 1e6;
+			printf("%d frames, %.1f fps\n", frame, 100.0 / dt);
+			t0 = t1;
+		}
+		if (secs > 0) {
+			gettimeofday(&t1, NULL);
+			if ((t1.tv_sec - tstart.tv_sec) +
+			    (t1.tv_usec - tstart.tv_usec) / 1e6 >= secs)
+				break;
+		}
+	}
+
+	printf("teapot done after %d frames\n", frame);
+	vrMesaDestroyContext(ctx);
+	free(mesh);
+	return 0;
+}
diff --git a/examples/teapot_data.inc b/examples/teapot_data.inc
new file mode 100644
index 0000000..eb89c04
--- /dev/null
+++ b/examples/teapot_data.inc
@@ -0,0 +1,192 @@
+	{ /* patch 1 */
+		{ { -80.000f,   0.000f,  30.000f}, { -80.000f, -44.800f,  30.000f}, { -44.800f, -80.000f,  30.000f}, {   0.000f, -80.000f,  30.000f} },
+		{ { -80.000f,   0.000f,  12.000f}, { -80.000f, -44.800f,  12.000f}, { -44.800f, -80.000f,  12.000f}, {   0.000f, -80.000f,  12.000f} },
+		{ { -60.000f,   0.000f,   3.000f}, { -60.000f, -33.600f,   3.000f}, { -33.600f, -60.000f,   3.000f}, {   0.000f, -60.000f,   3.000f} },
+		{ { -60.000f,   0.000f,   0.000f}, { -60.000f, -33.600f,   0.000f}, { -33.600f, -60.000f,   0.000f}, {   0.000f, -60.000f,   0.000f} },
+	},
+	{ /* patch 2 */
+		{ {   0.000f, -80.000f,  30.000f}, {  44.800f, -80.000f,  30.000f}, {  80.000f, -44.800f,  30.000f}, {  80.000f,   0.000f,  30.000f} },
+		{ {   0.000f, -80.000f,  12.000f}, {  44.800f, -80.000f,  12.000f}, {  80.000f, -44.800f,  12.000f}, {  80.000f,   0.000f,  12.000f} },
+		{ {   0.000f, -60.000f,   3.000f}, {  33.600f, -60.000f,   3.000f}, {  60.000f, -33.600f,   3.000f}, {  60.000f,   0.000f,   3.000f} },
+		{ {   0.000f, -60.000f,   0.000f}, {  33.600f, -60.000f,   0.000f}, {  60.000f, -33.600f,   0.000f}, {  60.000f,   0.000f,   0.000f} },
+	},
+	{ /* patch 3 */
+		{ { -60.000f,   0.000f,  90.000f}, { -60.000f, -33.600f,  90.000f}, { -33.600f, -60.000f,  90.000f}, {   0.000f, -60.000f,  90.000f} },
+		{ { -70.000f,   0.000f,  69.000f}, { -70.000f, -39.200f,  69.000f}, { -39.200f, -70.000f,  69.000f}, {   0.000f, -70.000f,  69.000f} },
+		{ { -80.000f,   0.000f,  48.000f}, { -80.000f, -44.800f,  48.000f}, { -44.800f, -80.000f,  48.000f}, {   0.000f, -80.000f,  48.000f} },
+		{ { -80.000f,   0.000f,  30.000f}, { -80.000f, -44.800f,  30.000f}, { -44.800f, -80.000f,  30.000f}, {   0.000f, -80.000f,  30.000f} },
+	},
+	{ /* patch 4 */
+		{ {   0.000f, -60.000f,  90.000f}, {  33.600f, -60.000f,  90.000f}, {  60.000f, -33.600f,  90.000f}, {  60.000f,   0.000f,  90.000f} },
+		{ {   0.000f, -70.000f,  69.000f}, {  39.200f, -70.000f,  69.000f}, {  70.000f, -39.200f,  69.000f}, {  70.000f,   0.000f,  69.000f} },
+		{ {   0.000f, -80.000f,  48.000f}, {  44.800f, -80.000f,  48.000f}, {  80.000f, -44.800f,  48.000f}, {  80.000f,   0.000f,  48.000f} },
+		{ {   0.000f, -80.000f,  30.000f}, {  44.800f, -80.000f,  30.000f}, {  80.000f, -44.800f,  30.000f}, {  80.000f,   0.000f,  30.000f} },
+	},
+	{ /* patch 5 */
+		{ { -56.000f,   0.000f,  90.000f}, { -56.000f, -31.360f,  90.000f}, { -31.360f, -56.000f,  90.000f}, {   0.000f, -56.000f,  90.000f} },
+		{ { -53.500f,   0.000f,  95.250f}, { -53.500f, -29.960f,  95.250f}, { -29.960f, -53.500f,  95.250f}, {   0.000f, -53.500f,  95.250f} },
+		{ { -57.500f,   0.000f,  95.250f}, { -57.500f, -32.200f,  95.250f}, { -32.200f, -57.500f,  95.250f}, {   0.000f, -57.500f,  95.250f} },
+		{ { -60.000f,   0.000f,  90.000f}, { -60.000f, -33.600f,  90.000f}, { -33.600f, -60.000f,  90.000f}, {   0.000f, -60.000f,  90.000f} },
+	},
+	{ /* patch 6 */
+		{ {   0.000f, -56.000f,  90.000f}, {  31.360f, -56.000f,  90.000f}, {  56.000f, -31.360f,  90.000f}, {  56.000f,   0.000f,  90.000f} },
+		{ {   0.000f, -53.500f,  95.250f}, {  29.960f, -53.500f,  95.250f}, {  53.500f, -29.960f,  95.250f}, {  53.500f,   0.000f,  95.250f} },
+		{ {   0.000f, -57.500f,  95.250f}, {  32.200f, -57.500f,  95.250f}, {  57.500f, -32.200f,  95.250f}, {  57.500f,   0.000f,  95.250f} },
+		{ {   0.000f, -60.000f,  90.000f}, {  33.600f, -60.000f,  90.000f}, {  60.000f, -33.600f,  90.000f}, {  60.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 7 */
+		{ {  80.000f,   0.000f,  30.000f}, {  80.000f,  44.800f,  30.000f}, {  44.800f,  80.000f,  30.000f}, {   0.000f,  80.000f,  30.000f} },
+		{ {  80.000f,   0.000f,  12.000f}, {  80.000f,  44.800f,  12.000f}, {  44.800f,  80.000f,  12.000f}, {   0.000f,  80.000f,  12.000f} },
+		{ {  60.000f,   0.000f,   3.000f}, {  60.000f,  33.600f,   3.000f}, {  33.600f,  60.000f,   3.000f}, {   0.000f,  60.000f,   3.000f} },
+		{ {  60.000f,   0.000f,   0.000f}, {  60.000f,  33.600f,   0.000f}, {  33.600f,  60.000f,   0.000f}, {   0.000f,  60.000f,   0.000f} },
+	},
+	{ /* patch 8 */
+		{ {   0.000f,  80.000f,  30.000f}, { -44.800f,  80.000f,  30.000f}, { -80.000f,  44.800f,  30.000f}, { -80.000f,   0.000f,  30.000f} },
+		{ {   0.000f,  80.000f,  12.000f}, { -44.800f,  80.000f,  12.000f}, { -80.000f,  44.800f,  12.000f}, { -80.000f,   0.000f,  12.000f} },
+		{ {   0.000f,  60.000f,   3.000f}, { -33.600f,  60.000f,   3.000f}, { -60.000f,  33.600f,   3.000f}, { -60.000f,   0.000f,   3.000f} },
+		{ {   0.000f,  60.000f,   0.000f}, { -33.600f,  60.000f,   0.000f}, { -60.000f,  33.600f,   0.000f}, { -60.000f,   0.000f,   0.000f} },
+	},
+	{ /* patch 9 */
+		{ {  60.000f,   0.000f,  90.000f}, {  60.000f,  33.600f,  90.000f}, {  33.600f,  60.000f,  90.000f}, {   0.000f,  60.000f,  90.000f} },
+		{ {  70.000f,   0.000f,  69.000f}, {  70.000f,  39.200f,  69.000f}, {  39.200f,  70.000f,  69.000f}, {   0.000f,  70.000f,  69.000f} },
+		{ {  80.000f,   0.000f,  48.000f}, {  80.000f,  44.800f,  48.000f}, {  44.800f,  80.000f,  48.000f}, {   0.000f,  80.000f,  48.000f} },
+		{ {  80.000f,   0.000f,  30.000f}, {  80.000f,  44.800f,  30.000f}, {  44.800f,  80.000f,  30.000f}, {   0.000f,  80.000f,  30.000f} },
+	},
+	{ /* patch 10 */
+		{ {   0.000f,  60.000f,  90.000f}, { -33.600f,  60.000f,  90.000f}, { -60.000f,  33.600f,  90.000f}, { -60.000f,   0.000f,  90.000f} },
+		{ {   0.000f,  70.000f,  69.000f}, { -39.200f,  70.000f,  69.000f}, { -70.000f,  39.200f,  69.000f}, { -70.000f,   0.000f,  69.000f} },
+		{ {   0.000f,  80.000f,  48.000f}, { -44.800f,  80.000f,  48.000f}, { -80.000f,  44.800f,  48.000f}, { -80.000f,   0.000f,  48.000f} },
+		{ {   0.000f,  80.000f,  30.000f}, { -44.800f,  80.000f,  30.000f}, { -80.000f,  44.800f,  30.000f}, { -80.000f,   0.000f,  30.000f} },
+	},
+	{ /* patch 11 */
+		{ {  56.000f,   0.000f,  90.000f}, {  56.000f,  31.360f,  90.000f}, {  31.360f,  56.000f,  90.000f}, {   0.000f,  56.000f,  90.000f} },
+		{ {  53.500f,   0.000f,  95.250f}, {  53.500f,  29.960f,  95.250f}, {  29.960f,  53.500f,  95.250f}, {   0.000f,  53.500f,  95.250f} },
+		{ {  57.500f,   0.000f,  95.250f}, {  57.500f,  32.200f,  95.250f}, {  32.200f,  57.500f,  95.250f}, {   0.000f,  57.500f,  95.250f} },
+		{ {  60.000f,   0.000f,  90.000f}, {  60.000f,  33.600f,  90.000f}, {  33.600f,  60.000f,  90.000f}, {   0.000f,  60.000f,  90.000f} },
+	},
+	{ /* patch 12 */
+		{ {   0.000f,  56.000f,  90.000f}, { -31.360f,  56.000f,  90.000f}, { -56.000f,  31.360f,  90.000f}, { -56.000f,   0.000f,  90.000f} },
+		{ {   0.000f,  53.500f,  95.250f}, { -29.960f,  53.500f,  95.250f}, { -53.500f,  29.960f,  95.250f}, { -53.500f,   0.000f,  95.250f} },
+		{ {   0.000f,  57.500f,  95.250f}, { -32.200f,  57.500f,  95.250f}, { -57.500f,  32.200f,  95.250f}, { -57.500f,   0.000f,  95.250f} },
+		{ {   0.000f,  60.000f,  90.000f}, { -33.600f,  60.000f,  90.000f}, { -60.000f,  33.600f,  90.000f}, { -60.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 13 */
+		{ { -64.000f,   0.000f,  75.000f}, { -64.000f,  12.000f,  75.000f}, { -60.000f,  12.000f,  84.000f}, { -60.000f,   0.000f,  84.000f} },
+		{ { -92.000f,   0.000f,  75.000f}, { -92.000f,  12.000f,  75.000f}, {-100.000f,  12.000f,  84.000f}, {-100.000f,   0.000f,  84.000f} },
+		{ {-108.000f,   0.000f,  75.000f}, {-108.000f,  12.000f,  75.000f}, {-120.000f,  12.000f,  84.000f}, {-120.000f,   0.000f,  84.000f} },
+		{ {-108.000f,   0.000f,  66.000f}, {-108.000f,  12.000f,  66.000f}, {-120.000f,  12.000f,  66.000f}, {-120.000f,   0.000f,  66.000f} },
+	},
+	{ /* patch 14 */
+		{ { -60.000f,   0.000f,  84.000f}, { -60.000f, -12.000f,  84.000f}, { -64.000f, -12.000f,  75.000f}, { -64.000f,   0.000f,  75.000f} },
+		{ {-100.000f,   0.000f,  84.000f}, {-100.000f, -12.000f,  84.000f}, { -92.000f, -12.000f,  75.000f}, { -92.000f,   0.000f,  75.000f} },
+		{ {-120.000f,   0.000f,  84.000f}, {-120.000f, -12.000f,  84.000f}, {-108.000f, -12.000f,  75.000f}, {-108.000f,   0.000f,  75.000f} },
+		{ {-120.000f,   0.000f,  66.000f}, {-120.000f, -12.000f,  66.000f}, {-108.000f, -12.000f,  66.000f}, {-108.000f,   0.000f,  66.000f} },
+	},
+	{ /* patch 15 */
+		{ {-108.000f,   0.000f,  66.000f}, {-108.000f,  12.000f,  66.000f}, {-120.000f,  12.000f,  66.000f}, {-120.000f,   0.000f,  66.000f} },
+		{ {-108.000f,   0.000f,  57.000f}, {-108.000f,  12.000f,  57.000f}, {-120.000f,  12.000f,  48.000f}, {-120.000f,   0.000f,  48.000f} },
+		{ {-100.000f,   0.000f,  39.000f}, {-100.000f,  12.000f,  39.000f}, {-106.000f,  12.000f,  31.500f}, {-106.000f,   0.000f,  31.500f} },
+		{ { -80.000f,   0.000f,  30.000f}, { -80.000f,  12.000f,  30.000f}, { -76.000f,  12.000f,  18.000f}, { -76.000f,   0.000f,  18.000f} },
+	},
+	{ /* patch 16 */
+		{ {-120.000f,   0.000f,  66.000f}, {-120.000f, -12.000f,  66.000f}, {-108.000f, -12.000f,  66.000f}, {-108.000f,   0.000f,  66.000f} },
+		{ {-120.000f,   0.000f,  48.000f}, {-120.000f, -12.000f,  48.000f}, {-108.000f, -12.000f,  57.000f}, {-108.000f,   0.000f,  57.000f} },
+		{ {-106.000f,   0.000f,  31.500f}, {-106.000f, -12.000f,  31.500f}, {-100.000f, -12.000f,  39.000f}, {-100.000f,   0.000f,  39.000f} },
+		{ { -76.000f,   0.000f,  18.000f}, { -76.000f, -12.000f,  18.000f}, { -80.000f, -12.000f,  30.000f}, { -80.000f,   0.000f,  30.000f} },
+	},
+	{ /* patch 17 */
+		{ {  68.000f,   0.000f,  51.000f}, {  68.000f,  26.400f,  51.000f}, {  68.000f,  26.400f,  18.000f}, {  68.000f,   0.000f,  18.000f} },
+		{ { 104.000f,   0.000f,  51.000f}, { 104.000f,  26.400f,  51.000f}, { 124.000f,  26.400f,  27.000f}, { 124.000f,   0.000f,  27.000f} },
+		{ {  92.000f,   0.000f,  78.000f}, {  92.000f,  10.000f,  78.000f}, {  96.000f,  10.000f,  75.000f}, {  96.000f,   0.000f,  75.000f} },
+		{ { 108.000f,   0.000f,  90.000f}, { 108.000f,  10.000f,  90.000f}, { 132.000f,  10.000f,  90.000f}, { 132.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 18 */
+		{ {  68.000f,   0.000f,  18.000f}, {  68.000f, -26.400f,  18.000f}, {  68.000f, -26.400f,  51.000f}, {  68.000f,   0.000f,  51.000f} },
+		{ { 124.000f,   0.000f,  27.000f}, { 124.000f, -26.400f,  27.000f}, { 104.000f, -26.400f,  51.000f}, { 104.000f,   0.000f,  51.000f} },
+		{ {  96.000f,   0.000f,  75.000f}, {  96.000f, -10.000f,  75.000f}, {  92.000f, -10.000f,  78.000f}, {  92.000f,   0.000f,  78.000f} },
+		{ { 132.000f,   0.000f,  90.000f}, { 132.000f, -10.000f,  90.000f}, { 108.000f, -10.000f,  90.000f}, { 108.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 19 */
+		{ { 108.000f,   0.000f,  90.000f}, { 108.000f,  10.000f,  90.000f}, { 132.000f,  10.000f,  90.000f}, { 132.000f,   0.000f,  90.000f} },
+		{ { 112.000f,   0.000f,  93.000f}, { 112.000f,  10.000f,  93.000f}, { 141.000f,  10.000f,  93.750f}, { 141.000f,   0.000f,  93.750f} },
+		{ { 116.000f,   0.000f,  93.000f}, { 116.000f,   6.000f,  93.000f}, { 138.000f,   6.000f,  94.500f}, { 138.000f,   0.000f,  94.500f} },
+		{ { 112.000f,   0.000f,  90.000f}, { 112.000f,   6.000f,  90.000f}, { 128.000f,   6.000f,  90.000f}, { 128.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 20 */
+		{ { 132.000f,   0.000f,  90.000f}, { 132.000f, -10.000f,  90.000f}, { 108.000f, -10.000f,  90.000f}, { 108.000f,   0.000f,  90.000f} },
+		{ { 141.000f,   0.000f,  93.750f}, { 141.000f, -10.000f,  93.750f}, { 112.000f, -10.000f,  93.000f}, { 112.000f,   0.000f,  93.000f} },
+		{ { 138.000f,   0.000f,  94.500f}, { 138.000f,  -6.000f,  94.500f}, { 116.000f,  -6.000f,  93.000f}, { 116.000f,   0.000f,  93.000f} },
+		{ { 128.000f,   0.000f,  90.000f}, { 128.000f,  -6.000f,  90.000f}, { 112.000f,  -6.000f,  90.000f}, { 112.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 21 */
+		{ {  50.000f,   0.000f,  90.000f}, {  50.000f,  28.000f,  90.000f}, {  28.000f,  50.000f,  90.000f}, {   0.000f,  50.000f,  90.000f} },
+		{ {  52.000f,   0.000f,  90.000f}, {  52.000f,  29.120f,  90.000f}, {  29.120f,  52.000f,  90.000f}, {   0.000f,  52.000f,  90.000f} },
+		{ {  54.000f,   0.000f,  90.000f}, {  54.000f,  30.240f,  90.000f}, {  30.240f,  54.000f,  90.000f}, {   0.000f,  54.000f,  90.000f} },
+		{ {  56.000f,   0.000f,  90.000f}, {  56.000f,  31.360f,  90.000f}, {  31.360f,  56.000f,  90.000f}, {   0.000f,  56.000f,  90.000f} },
+	},
+	{ /* patch 22 */
+		{ {   0.000f,  50.000f,  90.000f}, { -28.000f,  50.000f,  90.000f}, { -50.000f,  28.000f,  90.000f}, { -50.000f,   0.000f,  90.000f} },
+		{ {   0.000f,  52.000f,  90.000f}, { -29.120f,  52.000f,  90.000f}, { -52.000f,  29.120f,  90.000f}, { -52.000f,   0.000f,  90.000f} },
+		{ {   0.000f,  54.000f,  90.000f}, { -30.240f,  54.000f,  90.000f}, { -54.000f,  30.240f,  90.000f}, { -54.000f,   0.000f,  90.000f} },
+		{ {   0.000f,  56.000f,  90.000f}, { -31.360f,  56.000f,  90.000f}, { -56.000f,  31.360f,  90.000f}, { -56.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 23 */
+		{ { -50.000f,   0.000f,  90.000f}, { -50.000f, -28.000f,  90.000f}, { -28.000f, -50.000f,  90.000f}, {   0.000f, -50.000f,  90.000f} },
+		{ { -52.000f,   0.000f,  90.000f}, { -52.000f, -29.120f,  90.000f}, { -29.120f, -52.000f,  90.000f}, {   0.000f, -52.000f,  90.000f} },
+		{ { -54.000f,   0.000f,  90.000f}, { -54.000f, -30.240f,  90.000f}, { -30.240f, -54.000f,  90.000f}, {   0.000f, -54.000f,  90.000f} },
+		{ { -56.000f,   0.000f,  90.000f}, { -56.000f, -31.360f,  90.000f}, { -31.360f, -56.000f,  90.000f}, {   0.000f, -56.000f,  90.000f} },
+	},
+	{ /* patch 24 */
+		{ {   0.000f, -50.000f,  90.000f}, {  28.000f, -50.000f,  90.000f}, {  50.000f, -28.000f,  90.000f}, {  50.000f,   0.000f,  90.000f} },
+		{ {   0.000f, -52.000f,  90.000f}, {  29.120f, -52.000f,  90.000f}, {  52.000f, -29.120f,  90.000f}, {  52.000f,   0.000f,  90.000f} },
+		{ {   0.000f, -54.000f,  90.000f}, {  30.240f, -54.000f,  90.000f}, {  54.000f, -30.240f,  90.000f}, {  54.000f,   0.000f,  90.000f} },
+		{ {   0.000f, -56.000f,  90.000f}, {  31.360f, -56.000f,  90.000f}, {  56.000f, -31.360f,  90.000f}, {  56.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 25 */
+		{ {   8.000f,   0.000f, 102.000f}, {   8.000f,   4.480f, 102.000f}, {   4.480f,   8.000f, 102.000f}, {   0.000f,   8.000f, 102.000f} },
+		{ {  16.000f,   0.000f,  96.000f}, {  16.000f,   8.960f,  96.000f}, {   8.960f,  16.000f,  96.000f}, {   0.000f,  16.000f,  96.000f} },
+		{ {  52.000f,   0.000f,  96.000f}, {  52.000f,  29.120f,  96.000f}, {  29.120f,  52.000f,  96.000f}, {   0.000f,  52.000f,  96.000f} },
+		{ {  52.000f,   0.000f,  90.000f}, {  52.000f,  29.120f,  90.000f}, {  29.120f,  52.000f,  90.000f}, {   0.000f,  52.000f,  90.000f} },
+	},
+	{ /* patch 26 */
+		{ {   0.000f,   8.000f, 102.000f}, {  -4.480f,   8.000f, 102.000f}, {  -8.000f,   4.480f, 102.000f}, {  -8.000f,   0.000f, 102.000f} },
+		{ {   0.000f,  16.000f,  96.000f}, {  -8.960f,  16.000f,  96.000f}, { -16.000f,   8.960f,  96.000f}, { -16.000f,   0.000f,  96.000f} },
+		{ {   0.000f,  52.000f,  96.000f}, { -29.120f,  52.000f,  96.000f}, { -52.000f,  29.120f,  96.000f}, { -52.000f,   0.000f,  96.000f} },
+		{ {   0.000f,  52.000f,  90.000f}, { -29.120f,  52.000f,  90.000f}, { -52.000f,  29.120f,  90.000f}, { -52.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 27 */
+		{ {  -8.000f,   0.000f, 102.000f}, {  -8.000f,  -4.480f, 102.000f}, {  -4.480f,  -8.000f, 102.000f}, {   0.000f,  -8.000f, 102.000f} },
+		{ { -16.000f,   0.000f,  96.000f}, { -16.000f,  -8.960f,  96.000f}, {  -8.960f, -16.000f,  96.000f}, {   0.000f, -16.000f,  96.000f} },
+		{ { -52.000f,   0.000f,  96.000f}, { -52.000f, -29.120f,  96.000f}, { -29.120f, -52.000f,  96.000f}, {   0.000f, -52.000f,  96.000f} },
+		{ { -52.000f,   0.000f,  90.000f}, { -52.000f, -29.120f,  90.000f}, { -29.120f, -52.000f,  90.000f}, {   0.000f, -52.000f,  90.000f} },
+	},
+	{ /* patch 28 */
+		{ {   0.000f,  -8.000f, 102.000f}, {   4.480f,  -8.000f, 102.000f}, {   8.000f,  -4.480f, 102.000f}, {   8.000f,   0.000f, 102.000f} },
+		{ {   0.000f, -16.000f,  96.000f}, {   8.960f, -16.000f,  96.000f}, {  16.000f,  -8.960f,  96.000f}, {  16.000f,   0.000f,  96.000f} },
+		{ {   0.000f, -52.000f,  96.000f}, {  29.120f, -52.000f,  96.000f}, {  52.000f, -29.120f,  96.000f}, {  52.000f,   0.000f,  96.000f} },
+		{ {   0.000f, -52.000f,  90.000f}, {  29.120f, -52.000f,  90.000f}, {  52.000f, -29.120f,  90.000f}, {  52.000f,   0.000f,  90.000f} },
+	},
+	{ /* patch 29 */
+		{ {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f} },
+		{ {  32.000f,   0.000f, 120.000f}, {  32.000f,  18.000f, 120.000f}, {  18.000f,  32.000f, 120.000f}, {   0.000f,  32.000f, 120.000f} },
+		{ {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f} },
+		{ {   8.000f,   0.000f, 102.000f}, {   8.000f,   4.480f, 102.000f}, {   4.480f,   8.000f, 102.000f}, {   0.000f,   8.000f, 102.000f} },
+	},
+	{ /* patch 30 */
+		{ {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f} },
+		{ {   0.000f,  32.000f, 120.000f}, { -18.000f,  32.000f, 120.000f}, { -32.000f,  18.000f, 120.000f}, { -32.000f,   0.000f, 120.000f} },
+		{ {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f} },
+		{ {   0.000f,   8.000f, 102.000f}, {  -4.480f,   8.000f, 102.000f}, {  -8.000f,   4.480f, 102.000f}, {  -8.000f,   0.000f, 102.000f} },
+	},
+	{ /* patch 31 */
+		{ {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f} },
+		{ { -32.000f,   0.000f, 120.000f}, { -32.000f, -18.000f, 120.000f}, { -18.000f, -32.000f, 120.000f}, {   0.000f, -32.000f, 120.000f} },
+		{ {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f} },
+		{ {  -8.000f,   0.000f, 102.000f}, {  -8.000f,  -4.480f, 102.000f}, {  -4.480f,  -8.000f, 102.000f}, {   0.000f,  -8.000f, 102.000f} },
+	},
+	{ /* patch 32 */
+		{ {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f}, {   0.000f,   0.000f, 120.000f} },
+		{ {   0.000f, -32.000f, 120.000f}, {  18.000f, -32.000f, 120.000f}, {  32.000f, -18.000f, 120.000f}, {  32.000f,   0.000f, 120.000f} },
+		{ {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f}, {   0.000f,   0.000f, 108.000f} },
+		{ {   0.000f,  -8.000f, 102.000f}, {   4.480f,  -8.000f, 102.000f}, {   8.000f,  -4.480f, 102.000f}, {   8.000f,   0.000f, 102.000f} },
+	},