mesh_primitive_uv_sphere.cc

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/* SPDX-FileCopyrightText: 2023 Blender Authors
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */
 
#include <cmath>
 
#include "BLI_math_numbers.hh"
 
#include "BKE_attribute.hh"
#include "BKE_mesh.hh"
 
#include "GEO_mesh_primitive_uv_sphere.hh"
 
namespace blender::geometry {
 
Bounds<float3> calculate_bounds_radial_primitive(const float radius_top,
                                                 const float radius_bottom,
                                                 const int segments,
                                                 const float height)
{
  const float radius = std::max(radius_top, radius_bottom);
  const float delta_phi = (2.0f * math::numbers::pi) / float(segments);
 
  const float x_max = radius;
  const float x_min = std::cos(std::round(0.5f * segments) * delta_phi) * radius;
  const float y_max = std::sin(std::round(0.25f * segments) * delta_phi) * radius;
  const float y_min = -y_max;
 
  const float3 bounds_min(x_min, y_min, -height);
  const float3 bounds_max(x_max, y_max, height);
 
  return {bounds_min, bounds_max};
}
 
static int sphere_vert_total(const int segments, const int rings)
{
  return segments * (rings - 1) + 2;
}
 
static int sphere_edge_total(const int segments, const int rings)
{
  return segments * (rings * 2 - 1);
}
 
static int sphere_corner_total(const int segments, const int rings)
{
  const int quad_corners = 4 * segments * (rings - 2);
  const int tri_corners = 3 * segments * 2;
  return quad_corners + tri_corners;
}
 
static int sphere_face_total(const int segments, const int rings)
{
  const int quads = segments * (rings - 2);
  const int triangles = segments * 2;
  return quads + triangles;
}

BLI_NOINLINE static void calculate_sphere_vertex_data(MutableSpan<float3> positions,
                                                      MutableSpan<float3> vert_normals,
                                                      const float radius,
                                                      const int segments,
                                                      const int rings)
{
  const float delta_theta = math::numbers::pi / rings;
  const float delta_phi = (2.0f * math::numbers::pi) / segments;
 
  Array<float, 64> segment_cosines(segments + 1);
  for (const int segment : IndexRange(1, segments)) {
    const float phi = segment * delta_phi;
    segment_cosines[segment] = std::cos(phi);
  }
  Array<float, 64> segment_sines(segments + 1);
  for (const int segment : IndexRange(1, segments)) {
    const float phi = segment * delta_phi;
    segment_sines[segment] = std::sin(phi);
  }
 
  positions[0] = float3(0.0f, 0.0f, radius);
  vert_normals.first() = float3(0.0f, 0.0f, 1.0f);
 
  int vert_index = 1;
  for (const int ring : IndexRange(1, rings - 1)) {
    const float theta = ring * delta_theta;
    const float sin_theta = std::sin(theta);
    const float z = std::cos(theta);
    for (const int segment : IndexRange(1, segments)) {
      const float x = sin_theta * segment_cosines[segment];
      const float y = sin_theta * segment_sines[segment];
      positions[vert_index] = float3(x, y, z) * radius;
      vert_normals[vert_index] = float3(x, y, z);
      vert_index++;
    }
  }
 
  positions.last() = float3(0.0f, 0.0f, -radius);
  vert_normals.last() = float3(0.0f, 0.0f, -1.0f);
}
 
BLI_NOINLINE static void calculate_sphere_edge_indices(MutableSpan<int2> edges,
                                                       const int segments,
                                                       const int rings)
{
  int edge_index = 0;
 
  /* Add the edges connecting the top vertex to the first ring. */
  const int first_vert_ring_index_start = 1;
  for (const int segment : IndexRange(segments)) {
    int2 &edge = edges[edge_index++];
    edge[0] = 0;
    edge[1] = first_vert_ring_index_start + segment;
  }
 
  int ring_vert_index_start = 1;
  for (const int ring : IndexRange(rings - 1)) {
    const int next_ring_vert_index_start = ring_vert_index_start + segments;
 
    /* Add the edges running along each ring. */
    for (const int segment : IndexRange(segments)) {
      int2 &edge = edges[edge_index++];
      edge[0] = ring_vert_index_start + segment;
      edge[1] = ring_vert_index_start + ((segment + 1) % segments);
    }
 
    /* Add the edges connecting to the next ring. */
    if (ring < rings - 2) {
      for (const int segment : IndexRange(segments)) {
        int2 &edge = edges[edge_index++];
        edge[0] = ring_vert_index_start + segment;
        edge[1] = next_ring_vert_index_start + segment;
      }
    }
    ring_vert_index_start += segments;
  }
 
  /* Add the edges connecting the last ring to the bottom vertex. */
  const int last_vert_index = sphere_vert_total(segments, rings) - 1;
  const int last_vert_ring_start = last_vert_index - segments;
  for (const int segment : IndexRange(segments)) {
    int2 &edge = edges[edge_index++];
    edge[0] = last_vert_index;
    edge[1] = last_vert_ring_start + segment;
  }
}
 
BLI_NOINLINE static void calculate_sphere_faces(MutableSpan<int> face_offsets, const int segments)
{
  MutableSpan<int> face_sizes = face_offsets.drop_back(1);
  /* Add the triangles connected to the top vertex. */
  face_sizes.take_front(segments).fill(3);
  /* Add the middle quads. */
  face_sizes.drop_front(segments).drop_back(segments).fill(4);
  /* Add the triangles connected to the bottom vertex. */
  face_sizes.take_back(segments).fill(3);
 
  offset_indices::accumulate_counts_to_offsets(face_offsets);
}
 
BLI_NOINLINE static void calculate_sphere_corners(MutableSpan<int> corner_verts,
                                                  MutableSpan<int> corner_edges,
                                                  const int segments,
                                                  const int rings)
{
  auto segment_next_or_first = [&](const int segment) {
    return segment == segments - 1 ? 0 : segment + 1;
  };
 
  /* Add the triangles connected to the top vertex. */
  const int first_vert_ring_start = 1;
  for (const int segment : IndexRange(segments)) {
    const int loop_start = segment * 3;
    const int segment_next = segment_next_or_first(segment);
 
    corner_verts[loop_start + 0] = 0;
    corner_edges[loop_start + 0] = segment;
 
    corner_verts[loop_start + 1] = first_vert_ring_start + segment;
    corner_edges[loop_start + 1] = segments + segment;
 
    corner_verts[loop_start + 2] = first_vert_ring_start + segment_next;
    corner_edges[loop_start + 2] = segment_next;
  }
 
  const int rings_vert_start = 1;
  const int rings_edge_start = segments;
  const int rings_loop_start = segments * 3;
  for (const int ring : IndexRange(1, rings - 2)) {
    const int ring_vert_start = rings_vert_start + (ring - 1) * segments;
    const int ring_edge_start = rings_edge_start + (ring - 1) * segments * 2;
    const int ring_loop_start = rings_loop_start + (ring - 1) * segments * 4;
 
    const int next_ring_vert_start = ring_vert_start + segments;
    const int next_ring_edge_start = ring_edge_start + segments * 2;
    const int ring_vertical_edge_start = ring_edge_start + segments;
 
    for (const int segment : IndexRange(segments)) {
      const int loop_start = ring_loop_start + segment * 4;
      const int segment_next = segment_next_or_first(segment);
 
      corner_verts[loop_start + 0] = ring_vert_start + segment;
      corner_edges[loop_start + 0] = ring_vertical_edge_start + segment;
 
      corner_verts[loop_start + 1] = next_ring_vert_start + segment;
      corner_edges[loop_start + 1] = next_ring_edge_start + segment;
 
      corner_verts[loop_start + 2] = next_ring_vert_start + segment_next;
      corner_edges[loop_start + 2] = ring_vertical_edge_start + segment_next;
 
      corner_verts[loop_start + 3] = ring_vert_start + segment_next;
      corner_edges[loop_start + 3] = ring_edge_start + segment;
    }
  }
 
  /* Add the triangles connected to the bottom vertex. */
  const int bottom_loop_start = rings_loop_start + segments * (rings - 2) * 4;
  const int last_edge_ring_start = segments * (rings - 2) * 2 + segments;
  const int bottom_edge_fan_start = last_edge_ring_start + segments;
  const int last_vert_index = sphere_vert_total(segments, rings) - 1;
  const int last_vert_ring_start = last_vert_index - segments;
  for (const int segment : IndexRange(segments)) {
    const int loop_start = bottom_loop_start + segment * 3;
    const int segment_next = segment_next_or_first(segment);
 
    corner_verts[loop_start + 0] = last_vert_index;
    corner_edges[loop_start + 0] = bottom_edge_fan_start + segment_next;
 
    corner_verts[loop_start + 1] = last_vert_ring_start + segment_next;
    corner_edges[loop_start + 1] = last_edge_ring_start + segment;
 
    corner_verts[loop_start + 2] = last_vert_ring_start + segment;
    corner_edges[loop_start + 2] = bottom_edge_fan_start + segment;
  }
}
 
BLI_NOINLINE static void calculate_sphere_uvs(Mesh *mesh,
                                              const float segments,
                                              const float rings,
                                              const StringRef uv_map_id)
{
  bke::MutableAttributeAccessor attributes = mesh->attributes_for_write();
 
  bke::SpanAttributeWriter<float2> uv_attribute =
      attributes.lookup_or_add_for_write_only_span<float2>(uv_map_id, bke::AttrDomain::Corner);
  MutableSpan<float2> uvs = uv_attribute.span;
 
  const float dy = 1.0f / rings;
 
  const float segments_inv = 1.0f / segments;
 
  for (const int i_segment : IndexRange(segments)) {
    const int loop_start = i_segment * 3;
    const float segment = float(i_segment);
    uvs[loop_start + 0] = float2((segment + 0.5f) * segments_inv, 0.0f);
    uvs[loop_start + 1] = float2(segment * segments_inv, dy);
    uvs[loop_start + 2] = float2((segment + 1.0f) * segments_inv, dy);
  }
 
  const int rings_loop_start = segments * 3;
  for (const int i_ring : IndexRange(1, rings - 2)) {
    const int ring_loop_start = rings_loop_start + (i_ring - 1) * segments * 4;
    const float ring = float(i_ring);
    for (const int i_segment : IndexRange(segments)) {
      const int loop_start = ring_loop_start + i_segment * 4;
      const float segment = float(i_segment);
      uvs[loop_start + 0] = float2(segment * segments_inv, ring / rings);
      uvs[loop_start + 1] = float2(segment * segments_inv, (ring + 1.0f) / rings);
      uvs[loop_start + 2] = float2((segment + 1.0f) * segments_inv, (ring + 1.0f) / rings);
      uvs[loop_start + 3] = float2((segment + 1.0f) * segments_inv, ring / rings);
    }
  }
 
  const int bottom_loop_start = rings_loop_start + segments * (rings - 2) * 4;
  for (const int i_segment : IndexRange(segments)) {
    const int loop_start = bottom_loop_start + i_segment * 3;
    const float segment = float(i_segment);
    uvs[loop_start + 0] = float2((segment + 0.5f) * segments_inv, 1.0f);
    uvs[loop_start + 1] = float2((segment + 1.0f) * segments_inv, 1.0f - dy);
    uvs[loop_start + 2] = float2(segment * segments_inv, 1.0f - dy);
  }
 
  uv_attribute.finish();
}
 
static Bounds<float3> calculate_bounds_uv_sphere(const float radius,
                                                 const int segments,
                                                 const int rings)
{
  const float delta_theta = math::numbers::pi / float(rings);
  const float sin_equator = std::sin(std::round(0.5f * rings) * delta_theta);
 
  return calculate_bounds_radial_primitive(0.0f, radius * sin_equator, segments, radius);
}
 
Mesh *create_uv_sphere_mesh(const float radius,
                            const int segments,
                            const int rings,
                            const std::optional<StringRef> uv_map_id)
{
  Mesh *mesh = BKE_mesh_new_nomain(sphere_vert_total(segments, rings),
                                   sphere_edge_total(segments, rings),
                                   sphere_face_total(segments, rings),
                                   sphere_corner_total(segments, rings));
  MutableSpan<float3> positions = mesh->vert_positions_for_write();
  MutableSpan<int2> edges = mesh->edges_for_write();
  MutableSpan<int> face_offsets = mesh->face_offsets_for_write();
  MutableSpan<int> corner_verts = mesh->corner_verts_for_write();
  MutableSpan<int> corner_edges = mesh->corner_edges_for_write();
  bke::mesh_smooth_set(*mesh, false);
 
  threading::parallel_invoke(
      1024 < segments * rings,
      [&]() {
        Vector<float3> vert_normals(mesh->verts_num);
        calculate_sphere_vertex_data(positions, vert_normals, radius, segments, rings);
        bke::mesh_vert_normals_assign(*mesh, std::move(vert_normals));
      },
      [&]() { calculate_sphere_edge_indices(edges, segments, rings); },
      [&]() { calculate_sphere_faces(face_offsets, segments); },
      [&]() { calculate_sphere_corners(corner_verts, corner_edges, segments, rings); },
      [&]() {
        if (uv_map_id) {
          calculate_sphere_uvs(mesh, segments, rings, *uv_map_id);
        }
      });
 
  mesh->tag_loose_verts_none();
  mesh->tag_loose_edges_none();
  mesh->tag_overlapping_none();
  mesh->bounds_set_eager(calculate_bounds_uv_sphere(radius, segments, rings));
 
  return mesh;
}
 
}  // namespace blender::geometry