test/source/blender/blenkernel/intern/curve_poly.cc

/* SPDX-License-Identifier: GPL-2.0-or-later */

/** \file
 * \ingroup bke
 */

#include <algorithm>

#include "BLI_math_rotation.hh"
#include "BLI_math_vector.hh"

#include "BKE_curves.hh"

namespace blender::bke::curves::poly {

static float3 direction_bisect(const float3 &prev, const float3 &middle, const float3 &next)
{
  const float3 dir_prev = math::normalize(middle - prev);
  const float3 dir_next = math::normalize(next - middle);

  const float3 result = math::normalize(dir_prev + dir_next);
  if (UNLIKELY(math::is_zero(result))) {
    return float3(0.0f, 0.0f, 1.0f);
  }
  return result;
}

void calculate_tangents(const Span<float3> positions,
                        const bool is_cyclic,
                        MutableSpan<float3> tangents)
{
  BLI_assert(positions.size() == tangents.size());

  if (positions.size() == 1) {
    tangents.first() = float3(0.0f, 0.0f, 1.0f);
    return;
  }

  for (const int i : IndexRange(1, positions.size() - 2)) {
    tangents[i] = direction_bisect(positions[i - 1], positions[i], positions[i + 1]);
  }

  if (is_cyclic) {
    const float3 &second_to_last = positions[positions.size() - 2];
    const float3 &last = positions.last();
    const float3 &first = positions.first();
    const float3 &second = positions[1];
    tangents.first() = direction_bisect(last, first, second);
    tangents.last() = direction_bisect(second_to_last, last, first);
  }
  else {
    tangents.first() = math::normalize(positions[1] - positions.first());
    tangents.last() = math::normalize(positions.last() - positions[positions.size() - 2]);
  }
}

void calculate_normals_z_up(const Span<float3> tangents, MutableSpan<float3> normals)
{
  BLI_assert(normals.size() == tangents.size());

  /* Same as in `vec_to_quat`. */
  const float epsilon = 1e-4f;
  for (const int i : normals.index_range()) {
    const float3 &tangent = tangents[i];
    if (std::abs(tangent.x) + std::abs(tangent.y) < epsilon) {
      normals[i] = {1.0f, 0.0f, 0.0f};
    }
    else {
      normals[i] = math::normalize(float3(tangent.y, -tangent.x, 0.0f));
    }
  }
}

/**
 * Rotate the last normal in the same way the tangent has been rotated.
 */
static float3 calculate_next_normal(const float3 &last_normal,
                                    const float3 &last_tangent,
                                    const float3 &current_tangent)
{
  if (math::is_zero(last_tangent) || math::is_zero(current_tangent)) {
    return last_normal;
  }
  const float angle = angle_normalized_v3v3(last_tangent, current_tangent);
  if (angle != 0.0) {
    const float3 axis = math::normalize(math::cross(last_tangent, current_tangent));
    return math::rotate_direction_around_axis(last_normal, axis, angle);
  }
  return last_normal;
}

void calculate_normals_minimum(const Span<float3> tangents,
                               const bool cyclic,
                               MutableSpan<float3> normals)
{
  BLI_assert(normals.size() == tangents.size());

  if (normals.is_empty()) {
    return;
  }

  const float epsilon = 1e-4f;

  /* Set initial normal. */
  const float3 &first_tangent = tangents.first();
  if (fabs(first_tangent.x) + fabs(first_tangent.y) < epsilon) {
    normals.first() = {1.0f, 0.0f, 0.0f};
  }
  else {
    normals.first() = math::normalize(float3(first_tangent.y, -first_tangent.x, 0.0f));
  }

  /* Forward normal with minimum twist along the entire spline. */
  for (const int i : IndexRange(1, normals.size() - 1)) {
    normals[i] = calculate_next_normal(normals[i - 1], tangents[i - 1], tangents[i]);
  }

  if (!cyclic) {
    return;
  }

  /* Compute how much the first normal deviates from the normal that has been forwarded along the
   * entire cyclic spline. */
  const float3 uncorrected_last_normal = calculate_next_normal(
      normals.last(), tangents.last(), tangents.first());
  float correction_angle = angle_signed_on_axis_v3v3_v3(
      normals.first(), uncorrected_last_normal, tangents.first());
  if (correction_angle > M_PI) {
    correction_angle = correction_angle - 2 * M_PI;
  }

  /* Gradually apply correction by rotating all normals slightly. */
  const float angle_step = correction_angle / normals.size();
  for (const int i : normals.index_range()) {
    const float angle = angle_step * i;
    normals[i] = math::rotate_direction_around_axis(normals[i], tangents[i], angle);
  }
}

}  // namespace blender::bke::curves::poly