avfilter/vf_v360: add ball projection format

doc/filters.texi

@@ -18060,6 +18060,9 @@ If diagonal field of view is set it overrides horizontal and vertical field of v
 @item mercator
 Mercator format.
 
+@item ball
+Ball format, gives significant distortion toward the back.
+
 @end table
 
 @item interp

libavfilter/v360.h

@@ -40,6 +40,7 @@ enum Projections {
     CUBEMAP_1_6,
     STEREOGRAPHIC,
     MERCATOR,
+    BALL,
     NB_PROJECTIONS,
 };
 

libavfilter/vf_v360.c

@@ -66,6 +66,7 @@ static const AVOption v360_options[] = {
     {      "c1x6", "cubemap 1x6",                                0, AV_OPT_TYPE_CONST,  {.i64=CUBEMAP_1_6},     0,                   0, FLAGS, "in" },
     {        "sg", "stereographic",                              0, AV_OPT_TYPE_CONST,  {.i64=STEREOGRAPHIC},   0,                   0, FLAGS, "in" },
     {  "mercator", "mercator",                                   0, AV_OPT_TYPE_CONST,  {.i64=MERCATOR},        0,                   0, FLAGS, "in" },
+    {      "ball", "ball",                                       0, AV_OPT_TYPE_CONST,  {.i64=BALL},            0,                   0, FLAGS, "in" },
     {    "output", "set output projection",            OFFSET(out), AV_OPT_TYPE_INT,    {.i64=CUBEMAP_3_2},     0,    NB_PROJECTIONS-1, FLAGS, "out" },
     {         "e", "equirectangular",                            0, AV_OPT_TYPE_CONST,  {.i64=EQUIRECTANGULAR}, 0,                   0, FLAGS, "out" },
     {  "equirect", "equirectangular",                            0, AV_OPT_TYPE_CONST,  {.i64=EQUIRECTANGULAR}, 0,                   0, FLAGS, "out" },
@@ -81,6 +82,7 @@ static const AVOption v360_options[] = {
     {      "c1x6", "cubemap 1x6",                                0, AV_OPT_TYPE_CONST,  {.i64=CUBEMAP_1_6},     0,                   0, FLAGS, "out" },
     {        "sg", "stereographic",                              0, AV_OPT_TYPE_CONST,  {.i64=STEREOGRAPHIC},   0,                   0, FLAGS, "out" },
     {  "mercator", "mercator",                                   0, AV_OPT_TYPE_CONST,  {.i64=MERCATOR},        0,                   0, FLAGS, "out" },
+    {      "ball", "ball",                                       0, AV_OPT_TYPE_CONST,  {.i64=BALL},            0,                   0, FLAGS, "out" },
     {    "interp", "set interpolation method",      OFFSET(interp), AV_OPT_TYPE_INT,    {.i64=BILINEAR},        0, NB_INTERP_METHODS-1, FLAGS, "interp" },
     {      "near", "nearest neighbour",                          0, AV_OPT_TYPE_CONST,  {.i64=NEAREST},         0,                   0, FLAGS, "interp" },
     {   "nearest", "nearest neighbour",                          0, AV_OPT_TYPE_CONST,  {.i64=NEAREST},         0,                   0, FLAGS, "interp" },
@@ -1582,6 +1584,80 @@ static void mercator_to_xyz(const V360Context *s,
     vec[2] = -cos_theta * cos_phi;
 }
 
+/**
+ * Calculate frame position in ball format for corresponding 3D coordinates on sphere.
+ *
+ * @param s filter context
+ * @param vec coordinates on sphere
+ * @param width frame width
+ * @param height frame height
+ * @param us horizontal coordinates for interpolation window
+ * @param vs vertical coordinates for interpolation window
+ * @param du horizontal relative coordinate
+ * @param dv vertical relative coordinate
+ */
+static void xyz_to_ball(const V360Context *s,
+                        const float *vec, int width, int height,
+                        uint16_t us[4][4], uint16_t vs[4][4], float *du, float *dv)
+{
+    const float l = hypotf(vec[0], vec[1]);
+    const float r = sinf(acosf(-vec[2]) * 0.5f);
+    float uf, vf;
+    int ui, vi;
+
+    uf = (1.f - r * vec[0] / l) * width  / 2.f;
+    vf = (1.f + r * vec[1] / l) * height / 2.f;
+    ui = floorf(uf);
+    vi = floorf(vf);
+
+    *du = uf - ui;
+    *dv = vf - vi;
+
+    for (int i = -1; i < 3; i++) {
+        for (int j = -1; j < 3; j++) {
+            us[i + 1][j + 1] = mod(ui + j, width);
+            vs[i + 1][j + 1] = av_clip(vi + i, 0, height - 1);
+        }
+    }
+}
+
+/**
+ * Calculate 3D coordinates on sphere for corresponding frame position in ball format.
+ *
+ * @param s filter context
+ * @param i horizontal position on frame [0, width)
+ * @param j vertical position on frame [0, height)
+ * @param width frame width
+ * @param height frame height
+ * @param vec coordinates on sphere
+ */
+static void ball_to_xyz(const V360Context *s,
+                        int i, int j, int width, int height,
+                        float *vec)
+{
+    const float x = (2.f * i) / width  - 1.f;
+    const float y = (2.f * j) / height - 1.f;
+    const float l = hypotf(x, y);
+
+    if (l <= 1.f) {
+        const float phi   = atan2f(x, y);
+        const float theta = 2.f * asinf(l);
+
+        const float sin_phi   = sinf(phi);
+        const float cos_phi   = cosf(phi);
+        const float sin_theta = sinf(theta);
+        const float cos_theta = cosf(theta);
+
+        vec[0] =  sin_theta * sin_phi;
+        vec[1] = -sin_theta * cos_phi;
+        vec[2] = -cos_theta;
+    } else {
+        vec[0] =  0.f;
+        vec[1] = -1.f;
+        vec[2] =  0.f;
+    }
+}
+
 /**
  * Prepare data for processing equi-angular cubemap input format.
  *
@@ -2429,6 +2505,12 @@ static int config_output(AVFilterLink *outlink)
         wf = w;
         hf = h;
         break;
+    case BALL:
+        s->in_transform = xyz_to_ball;
+        err = 0;
+        wf = w;
+        hf = h / 2.f;
+        break;
     default:
         av_log(ctx, AV_LOG_ERROR, "Specified input format is not handled.\n");
         return AVERROR_BUG;
@@ -2499,6 +2581,12 @@ static int config_output(AVFilterLink *outlink)
         w = roundf(wf);
         h = roundf(hf);
         break;
+    case BALL:
+        s->out_transform = ball_to_xyz;
+        prepare_out = NULL;
+        w = roundf(wf);
+        h = roundf(hf * 2.f);
+        break;
     default:
         av_log(ctx, AV_LOG_ERROR, "Specified output format is not handled.\n");
         return AVERROR_BUG;