Curve2D/Curve3D: exact linear interpolation
While calculating interpolated points, intervals between two baked points has been assummed to be `baked_interval`. The assumption could cause significant error in some extreme cases (for example #7088). To improve accuracy, `baked_dist_cache` is introduced, which stores distance from starting point for each baked points. `interpolate_baked` now returns exact linear-interpolated position along baked points.
This commit is contained in:
Jihyun Yu
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@ -662,19 +662,27 @@ void Curve2D::_bake() const {
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if (points.size() == 0) {
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baked_point_cache.resize(0);
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baked_dist_cache.resize(0);
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return;
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}
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if (points.size() == 1) {
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baked_point_cache.resize(1);
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baked_point_cache.set(0, points[0].pos);
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baked_dist_cache.resize(1);
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baked_dist_cache.set(0, 0.0);
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return;
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}
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Vector2 pos = points[0].pos;
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float dist = 0.0;
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List<Vector2> pointlist;
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List<float> distlist;
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pointlist.push_back(pos); //start always from origin
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distlist.push_back(0.0);
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for (int i = 0; i < points.size() - 1; i++) {
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float step = 0.1; // at least 10 substeps ought to be enough?
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@ -712,7 +720,10 @@ void Curve2D::_bake() const {
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pos = npp;
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p = mid;
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dist += d;
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pointlist.push_back(pos);
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distlist.push_back(dist);
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} else {
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p = np;
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}
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@ -722,16 +733,20 @@ void Curve2D::_bake() const {
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Vector2 lastpos = points[points.size() - 1].pos;
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float rem = pos.distance_to(lastpos);
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baked_max_ofs = (pointlist.size() - 1) * bake_interval + rem;
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dist += rem;
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baked_max_ofs = dist;
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pointlist.push_back(lastpos);
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distlist.push_back(dist);
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baked_point_cache.resize(pointlist.size());
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Vector2 *w = baked_point_cache.ptrw();
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int idx = 0;
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baked_dist_cache.resize(distlist.size());
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for (const Vector2 &E : pointlist) {
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w[idx] = E;
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idx++;
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Vector2 *w = baked_point_cache.ptrw();
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float *wd = baked_dist_cache.ptrw();
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for (int i = 0; i < pointlist.size(); i++) {
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w[i] = pointlist[i];
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wd[i] = distlist[i];
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}
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}
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@ -766,19 +781,26 @@ Vector2 Curve2D::interpolate_baked(float p_offset, bool p_cubic) const {
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return r[bpc - 1];
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}
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int idx = Math::floor((double)p_offset / (double)bake_interval);
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float frac = Math::fmod(p_offset, (float)bake_interval);
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if (idx >= bpc - 1) {
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return r[bpc - 1];
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} else if (idx == bpc - 2) {
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if (frac > 0) {
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frac /= Math::fmod(baked_max_ofs, bake_interval);
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int start = 0, end = bpc, idx = (end + start) / 2;
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// binary search to find baked points
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while (start < idx) {
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float offset = baked_dist_cache[idx];
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if (p_offset <= offset) {
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end = idx;
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} else {
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start = idx;
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}
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} else {
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frac /= bake_interval;
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idx = (end + start) / 2;
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}
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float offset_begin = baked_dist_cache[idx];
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float offset_end = baked_dist_cache[idx + 1];
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float idx_interval = offset_end - offset_begin;
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ERR_FAIL_COND_V_MSG(p_offset < offset_begin || p_offset > offset_end, Vector2(), "failed to find baked segment");
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float frac = (p_offset - offset_begin) / idx_interval;
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if (p_cubic) {
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Vector2 pre = idx > 0 ? r[idx - 1] : r[idx];
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Vector2 post = (idx < (bpc - 2)) ? r[idx + 2] : r[idx + 1];
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@ -1145,6 +1167,7 @@ void Curve3D::_bake() const {
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baked_point_cache.resize(0);
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baked_tilt_cache.resize(0);
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baked_up_vector_cache.resize(0);
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baked_dist_cache.resize(0);
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return;
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}
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@ -1153,6 +1176,8 @@ void Curve3D::_bake() const {
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baked_point_cache.set(0, points[0].pos);
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baked_tilt_cache.resize(1);
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baked_tilt_cache.set(0, points[0].tilt);
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baked_dist_cache.resize(1);
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baked_dist_cache.set(0, 0.0);
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if (up_vector_enabled) {
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baked_up_vector_cache.resize(1);
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@ -1165,8 +1190,12 @@ void Curve3D::_bake() const {
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}
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Vector3 pos = points[0].pos;
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float dist = 0.0;
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List<Plane> pointlist;
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List<float> distlist;
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pointlist.push_back(Plane(pos, points[0].tilt));
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distlist.push_back(0.0);
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for (int i = 0; i < points.size() - 1; i++) {
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float step = 0.1; // at least 10 substeps ought to be enough?
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@ -1207,7 +1236,10 @@ void Curve3D::_bake() const {
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Plane post;
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post.normal = pos;
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post.d = Math::lerp(points[i].tilt, points[i + 1].tilt, mid);
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dist += d;
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pointlist.push_back(post);
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distlist.push_back(dist);
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} else {
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p = np;
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}
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@ -1218,8 +1250,10 @@ void Curve3D::_bake() const {
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float lastilt = points[points.size() - 1].tilt;
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float rem = pos.distance_to(lastpos);
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baked_max_ofs = (pointlist.size() - 1) * bake_interval + rem;
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dist += rem;
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baked_max_ofs = dist;
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pointlist.push_back(Plane(lastpos, lastilt));
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distlist.push_back(dist);
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baked_point_cache.resize(pointlist.size());
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Vector3 *w = baked_point_cache.ptrw();
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@ -1231,6 +1265,9 @@ void Curve3D::_bake() const {
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baked_up_vector_cache.resize(up_vector_enabled ? pointlist.size() : 0);
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Vector3 *up_write = baked_up_vector_cache.ptrw();
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baked_dist_cache.resize(pointlist.size());
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float *wd = baked_dist_cache.ptrw();
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Vector3 sideways;
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Vector3 up;
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Vector3 forward;
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@ -1242,6 +1279,7 @@ void Curve3D::_bake() const {
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for (const Plane &E : pointlist) {
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w[idx] = E.normal;
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wt[idx] = E.d;
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wd[idx] = distlist[idx];
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if (!up_vector_enabled) {
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idx++;
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@ -1308,19 +1346,26 @@ Vector3 Curve3D::interpolate_baked(float p_offset, bool p_cubic) const {
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return r[bpc - 1];
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}
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int idx = Math::floor((double)p_offset / (double)bake_interval);
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float frac = Math::fmod(p_offset, bake_interval);
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if (idx >= bpc - 1) {
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return r[bpc - 1];
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} else if (idx == bpc - 2) {
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if (frac > 0) {
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frac /= Math::fmod(baked_max_ofs, bake_interval);
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int start = 0, end = bpc, idx = (end + start) / 2;
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// binary search to find baked points
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while (start < idx) {
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float offset = baked_dist_cache[idx];
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if (p_offset <= offset) {
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end = idx;
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} else {
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start = idx;
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}
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} else {
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frac /= bake_interval;
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idx = (end + start) / 2;
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}
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float offset_begin = baked_dist_cache[idx];
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float offset_end = baked_dist_cache[idx + 1];
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float idx_interval = offset_end - offset_begin;
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ERR_FAIL_COND_V_MSG(p_offset < offset_begin || p_offset > offset_end, Vector3(), "failed to find baked segment");
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float frac = (p_offset - offset_begin) / idx_interval;
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if (p_cubic) {
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Vector3 pre = idx > 0 ? r[idx - 1] : r[idx];
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Vector3 post = (idx < (bpc - 2)) ? r[idx + 2] : r[idx + 1];
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@ -161,6 +161,7 @@ class Curve2D : public Resource {
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mutable bool baked_cache_dirty = false;
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mutable PackedVector2Array baked_point_cache;
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mutable PackedFloat32Array baked_dist_cache;
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mutable float baked_max_ofs = 0.0;
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void _bake() const;
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@ -224,6 +225,7 @@ class Curve3D : public Resource {
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mutable PackedVector3Array baked_point_cache;
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mutable Vector<real_t> baked_tilt_cache;
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mutable PackedVector3Array baked_up_vector_cache;
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mutable PackedFloat32Array baked_dist_cache;
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mutable float baked_max_ofs = 0.0;
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void _bake() const;
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@ -216,6 +216,41 @@ TEST_CASE("[Curve] Custom curve with linear tangents") {
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Math::is_equal_approx(curve->interpolate_baked(0.7), (real_t)0.8),
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"Custom free curve should return the expected baked value at offset 0.7 after removing point at invalid index 10.");
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}
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TEST_CASE("[Curve2D] Linear sampling should return exact value") {
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Ref<Curve2D> curve = memnew(Curve2D);
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int len = 2048;
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curve->add_point(Vector2(0, 0));
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curve->add_point(Vector2((float)len, 0));
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float baked_length = curve->get_baked_length();
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CHECK((float)len == baked_length);
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for (int i = 0; i < len; i++) {
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float expected = (float)i;
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Vector2 pos = curve->interpolate_baked(expected);
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CHECK_MESSAGE(pos.x == expected, "interpolate_baked should return exact value");
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}
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}
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TEST_CASE("[Curve3D] Linear sampling should return exact value") {
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Ref<Curve3D> curve = memnew(Curve3D);
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int len = 2048;
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curve->add_point(Vector3(0, 0, 0));
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curve->add_point(Vector3((float)len, 0, 0));
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float baked_length = curve->get_baked_length();
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CHECK((float)len == baked_length);
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for (int i = 0; i < len; i++) {
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float expected = (float)i;
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Vector3 pos = curve->interpolate_baked(expected);
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CHECK_MESSAGE(pos.x == expected, "interpolate_baked should return exact value");
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}
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}
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} // namespace TestCurve
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#endif // TEST_CURVE_H
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