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-rw-r--r--scene/resources/curve.cpp395
1 files changed, 250 insertions, 145 deletions
diff --git a/scene/resources/curve.cpp b/scene/resources/curve.cpp
index eda9af9dde..0c36abc148 100644
--- a/scene/resources/curve.cpp
+++ b/scene/resources/curve.cpp
@@ -31,6 +31,7 @@
#include "curve.h"
#include "core/core_string_names.h"
+#include "core/math/math_funcs.h"
const char *Curve::SIGNAL_RANGE_CHANGED = "range_changed";
@@ -1413,8 +1414,9 @@ void Curve3D::_bake() const {
if (points.size() == 0) {
baked_point_cache.clear();
baked_tilt_cache.clear();
- baked_up_vector_cache.clear();
baked_dist_cache.clear();
+
+ baked_up_vector_cache.clear();
return;
}
@@ -1438,15 +1440,16 @@ void Curve3D::_bake() const {
Vector3 position = points[0].position;
real_t dist = 0.0;
- List<Plane> pointlist;
+ List<Plane> pointlist; // Abuse Plane for (position, dist)
List<real_t> distlist;
// Start always from origin.
pointlist.push_back(Plane(position, points[0].tilt));
distlist.push_back(0.0);
+ // Step 1: Sample points
+ const real_t step = 0.1; // At least 10 substeps ought to be enough?
for (int i = 0; i < points.size() - 1; i++) {
- real_t step = 0.1; // at least 10 substeps ought to be enough?
real_t p = 0.0;
while (p < 1.0) {
@@ -1461,7 +1464,7 @@ void Curve3D::_bake() const {
if (d > bake_interval) {
// OK! between P and NP there _has_ to be Something, let's go searching!
- int iterations = 10; //lots of detail!
+ const int iterations = 10; // Lots of detail!
real_t low = p;
real_t hi = np;
@@ -1496,76 +1499,135 @@ void Curve3D::_bake() const {
Vector3 npp = points[i + 1].position;
real_t d = position.distance_to(npp);
- position = npp;
- Plane post;
- post.normal = position;
- post.d = points[i + 1].tilt;
+ if (d > CMP_EPSILON) { // Avoid the degenerate case of two very close points.
+ position = npp;
+ Plane post;
+ post.normal = position;
+ post.d = points[i + 1].tilt;
- dist += d;
+ dist += d;
- pointlist.push_back(post);
- distlist.push_back(dist);
+ pointlist.push_back(post);
+ distlist.push_back(dist);
+ }
}
baked_max_ofs = dist;
- baked_point_cache.resize(pointlist.size());
- Vector3 *w = baked_point_cache.ptrw();
- int idx = 0;
+ const int point_count = pointlist.size();
+ {
+ baked_point_cache.resize(point_count);
+ Vector3 *w = baked_point_cache.ptrw();
- baked_tilt_cache.resize(pointlist.size());
- real_t *wt = baked_tilt_cache.ptrw();
+ baked_tilt_cache.resize(point_count);
+ real_t *wt = baked_tilt_cache.ptrw();
- baked_up_vector_cache.resize(up_vector_enabled ? pointlist.size() : 0);
- Vector3 *up_write = baked_up_vector_cache.ptrw();
+ baked_dist_cache.resize(point_count);
+ real_t *wd = baked_dist_cache.ptrw();
- baked_dist_cache.resize(pointlist.size());
- real_t *wd = baked_dist_cache.ptrw();
+ int idx = 0;
+ for (const Plane &E : pointlist) {
+ w[idx] = E.normal;
+ wt[idx] = E.d;
+ wd[idx] = distlist[idx];
- Vector3 sideways;
- Vector3 up;
- Vector3 forward;
+ idx++;
+ }
+ }
+
+ if (!up_vector_enabled) {
+ baked_up_vector_cache.resize(0);
+ return;
+ }
- Vector3 prev_sideways = Vector3(1, 0, 0);
- Vector3 prev_up = Vector3(0, 1, 0);
- Vector3 prev_forward = Vector3(0, 0, 1);
+ // Step 2: Calculate the up vectors and the whole local reference frame
+ //
+ // See Dougan, Carl. "The parallel transport frame." Game Programming Gems 2 (2001): 215-219.
+ // for an example discussing about why not the Frenet frame.
+ {
+ PackedVector3Array forward_vectors;
- for (const Plane &E : pointlist) {
- w[idx] = E.normal;
- wt[idx] = E.d;
- wd[idx] = distlist[idx];
+ baked_up_vector_cache.resize(point_count);
+ forward_vectors.resize(point_count);
- if (!up_vector_enabled) {
- idx++;
- continue;
+ Vector3 *up_write = baked_up_vector_cache.ptrw();
+ Vector3 *forward_write = forward_vectors.ptrw();
+
+ const Vector3 *points_ptr = baked_point_cache.ptr();
+
+ Basis frame; // X-right, Y-up, Z-forward.
+ Basis frame_prev;
+
+ // Set the initial frame based on Y-up rule.
+ {
+ Vector3 up(0, 1, 0);
+ Vector3 forward = (points_ptr[1] - points_ptr[0]).normalized();
+ if (forward.is_equal_approx(Vector3())) {
+ forward = Vector3(1, 0, 0);
+ }
+
+ if (abs(forward.dot(up)) > 1.0 - UNIT_EPSILON) {
+ frame_prev = Basis::looking_at(-forward, up);
+ } else {
+ frame_prev = Basis::looking_at(-forward, Vector3(1, 0, 0));
+ }
+
+ up_write[0] = frame_prev.get_column(1);
+ forward_write[0] = frame_prev.get_column(2);
}
- forward = idx > 0 ? (w[idx] - w[idx - 1]).normalized() : prev_forward;
+ // Calculate the Parallel Transport Frame.
+ for (int idx = 1; idx < point_count; idx++) {
+ Vector3 forward = (points_ptr[idx] - points_ptr[idx - 1]).normalized();
+ if (forward.is_equal_approx(Vector3())) {
+ forward = frame_prev.get_column(2);
+ }
- real_t y_dot = prev_up.dot(forward);
+ Basis rotate;
+ rotate.rotate_to_align(frame_prev.get_column(2), forward);
+ frame = rotate * frame_prev;
+ frame.orthonormalize(); // guard against float error accumulation
- if (y_dot > (1.0f - CMP_EPSILON)) {
- sideways = prev_sideways;
- up = -prev_forward;
- } else if (y_dot < -(1.0f - CMP_EPSILON)) {
- sideways = prev_sideways;
- up = prev_forward;
- } else {
- sideways = prev_up.cross(forward).normalized();
- up = forward.cross(sideways).normalized();
+ up_write[idx] = frame.get_column(1);
+ forward_write[idx] = frame.get_column(2);
+
+ frame_prev = frame;
}
- if (idx == 1) {
- up_write[0] = up;
+ bool is_loop = true;
+ // Loop smoothing only applies when the curve is a loop, which means two ends meet, and share forward directions.
+ {
+ if (!points_ptr[0].is_equal_approx(points_ptr[point_count - 1])) {
+ is_loop = false;
+ }
+
+ real_t dot = forward_write[0].dot(forward_write[point_count - 1]);
+ if (dot < 1.0 - 0.01) { // Alignment should not be too tight, or it dosen't work for coarse bake interval
+ is_loop = false;
+ }
}
- up_write[idx] = up;
+ // Twist up vectors, so that they align at two ends of the curve.
+ if (is_loop) {
+ const Vector3 up_start = up_write[0];
+ const Vector3 up_end = up_write[point_count - 1];
+
+ real_t sign = SIGN(up_end.cross(up_start).dot(forward_write[0]));
+ real_t full_angle = Quaternion(up_end, up_start).get_angle();
- prev_sideways = sideways;
- prev_up = up;
- prev_forward = forward;
+ if (abs(full_angle) < UNIT_EPSILON) {
+ return;
+ } else {
+ const real_t *dists = baked_dist_cache.ptr();
+ for (int idx = 1; idx < point_count; idx++) {
+ const real_t frac = dists[idx] / baked_max_ofs;
+ const real_t angle = Math::lerp((real_t)0.0, full_angle, frac);
+ Basis twist(forward_write[idx] * sign, angle);
- idx++;
+ up_write[idx] = twist.xform(up_write[idx]);
+ }
+ }
+ }
}
}
@@ -1577,27 +1639,15 @@ real_t Curve3D::get_baked_length() const {
return baked_max_ofs;
}
-Vector3 Curve3D::sample_baked(real_t p_offset, bool p_cubic) const {
- if (baked_cache_dirty) {
- _bake();
- }
+Curve3D::Interval Curve3D::_find_interval(real_t p_offset) const {
+ Interval interval = {
+ -1,
+ 0.0
+ };
+ ERR_FAIL_COND_V_MSG(baked_cache_dirty, interval, "Backed cache is dirty");
- // Validate: Curve may not have baked points.
int pc = baked_point_cache.size();
- ERR_FAIL_COND_V_MSG(pc == 0, Vector3(), "No points in Curve3D.");
-
- if (pc == 1) {
- return baked_point_cache.get(0);
- }
-
- const Vector3 *r = baked_point_cache.ptr();
-
- if (p_offset < 0) {
- return r[0];
- }
- if (p_offset >= baked_max_ofs) {
- return r[pc - 1];
- }
+ ERR_FAIL_COND_V_MSG(pc < 2, interval, "Less than two points in cache");
int start = 0;
int end = pc;
@@ -1617,9 +1667,27 @@ Vector3 Curve3D::sample_baked(real_t p_offset, bool p_cubic) const {
real_t offset_end = baked_dist_cache[idx + 1];
real_t idx_interval = offset_end - offset_begin;
- ERR_FAIL_COND_V_MSG(p_offset < offset_begin || p_offset > offset_end, Vector3(), "Couldn't find baked segment.");
+ ERR_FAIL_COND_V_MSG(p_offset < offset_begin || p_offset > offset_end, interval, "Offset out of range.");
- real_t frac = (p_offset - offset_begin) / idx_interval;
+ interval.idx = idx;
+ if (idx_interval < FLT_EPSILON) {
+ interval.frac = 0.5; // For a very short interval, 0.5 is a reasonable choice.
+ ERR_FAIL_V_MSG(interval, "Zero length interval.");
+ }
+
+ interval.frac = (p_offset - offset_begin) / idx_interval;
+ return interval;
+}
+
+Vector3 Curve3D::_sample_baked(Interval p_interval, bool p_cubic) const {
+ // Assuming p_interval is valid.
+ ERR_FAIL_INDEX_V_MSG(p_interval.idx, baked_point_cache.size(), Vector3(), "Invalid interval");
+
+ int idx = p_interval.idx;
+ real_t frac = p_interval.frac;
+
+ const Vector3 *r = baked_point_cache.ptr();
+ int pc = baked_point_cache.size();
if (p_cubic) {
Vector3 pre = idx > 0 ? r[idx - 1] : r[idx];
@@ -1630,114 +1698,150 @@ Vector3 Curve3D::sample_baked(real_t p_offset, bool p_cubic) const {
}
}
-real_t Curve3D::sample_baked_tilt(real_t p_offset) const {
- if (baked_cache_dirty) {
- _bake();
- }
-
- // Validate: Curve may not have baked tilts.
- int pc = baked_tilt_cache.size();
- ERR_FAIL_COND_V_MSG(pc == 0, 0, "No tilts in Curve3D.");
+real_t Curve3D::_sample_baked_tilt(Interval p_interval) const {
+ // Assuming that p_interval is valid.
+ ERR_FAIL_INDEX_V_MSG(p_interval.idx, baked_tilt_cache.size(), 0.0, "Invalid interval");
- if (pc == 1) {
- return baked_tilt_cache.get(0);
- }
+ int idx = p_interval.idx;
+ real_t frac = p_interval.frac;
const real_t *r = baked_tilt_cache.ptr();
- if (p_offset < 0) {
- return r[0];
+ return Math::lerp(r[idx], r[idx + 1], frac);
+}
+
+Basis Curve3D::_sample_posture(Interval p_interval, bool p_apply_tilt) const {
+ // Assuming that p_interval is valid.
+ ERR_FAIL_INDEX_V_MSG(p_interval.idx, baked_point_cache.size(), Basis(), "Invalid interval");
+ if (up_vector_enabled) {
+ ERR_FAIL_INDEX_V_MSG(p_interval.idx, baked_up_vector_cache.size(), Basis(), "Invalid interval");
}
- if (p_offset >= baked_max_ofs) {
- return r[pc - 1];
+
+ int idx = p_interval.idx;
+ real_t frac = p_interval.frac;
+
+ Vector3 forward_begin;
+ Vector3 forward_end;
+ if (idx == 0) {
+ forward_begin = (baked_point_cache[1] - baked_point_cache[0]).normalized();
+ forward_end = (baked_point_cache[1] - baked_point_cache[0]).normalized();
+ } else {
+ forward_begin = (baked_point_cache[idx] - baked_point_cache[idx - 1]).normalized();
+ forward_end = (baked_point_cache[idx + 1] - baked_point_cache[idx]).normalized();
}
- int start = 0;
- int end = pc;
- int idx = (end + start) / 2;
- // Binary search to find baked points.
- while (start < idx) {
- real_t offset = baked_dist_cache[idx];
- if (p_offset <= offset) {
- end = idx;
- } else {
- start = idx;
- }
- idx = (end + start) / 2;
+ Vector3 up_begin;
+ Vector3 up_end;
+ if (up_vector_enabled) {
+ const Vector3 *up_ptr = baked_up_vector_cache.ptr();
+ up_begin = up_ptr[idx];
+ up_end = up_ptr[idx + 1];
+ } else {
+ up_begin = Vector3(0.0, 1.0, 0.0);
+ up_end = Vector3(0.0, 1.0, 0.0);
}
- real_t offset_begin = baked_dist_cache[idx];
- real_t offset_end = baked_dist_cache[idx + 1];
+ // Build frames at both ends of the interval, then interpolate.
+ const Basis frame_begin = Basis::looking_at(-forward_begin, up_begin);
+ const Basis frame_end = Basis::looking_at(-forward_end, up_end);
+ const Basis frame = frame_begin.slerp(frame_end, frac).orthonormalized();
- real_t idx_interval = offset_end - offset_begin;
- ERR_FAIL_COND_V_MSG(p_offset < offset_begin || p_offset > offset_end, 0, "Couldn't find baked segment.");
+ if (!p_apply_tilt) {
+ return frame;
+ }
- real_t frac = (p_offset - offset_begin) / idx_interval;
+ // Applying tilt.
+ const real_t tilt = _sample_baked_tilt(p_interval);
+ Vector3 forward = frame.get_column(2);
- return Math::lerp(r[idx], r[idx + 1], (real_t)frac);
+ const Basis twist(forward, tilt);
+ return twist * frame;
}
-Vector3 Curve3D::sample_baked_up_vector(real_t p_offset, bool p_apply_tilt) const {
+Vector3 Curve3D::sample_baked(real_t p_offset, bool p_cubic) const {
if (baked_cache_dirty) {
_bake();
}
- // Validate: Curve may not have baked up vectors.
- int count = baked_up_vector_cache.size();
- ERR_FAIL_COND_V_MSG(count == 0, Vector3(0, 1, 0), "No up vectors in Curve3D.");
+ // Validate: Curve may not have baked points.
+ int pc = baked_point_cache.size();
+ ERR_FAIL_COND_V_MSG(pc == 0, Vector3(), "No points in Curve3D.");
- if (count == 1) {
- return baked_up_vector_cache.get(0);
+ if (pc == 1) {
+ return baked_point_cache[0];
}
- const Vector3 *r = baked_up_vector_cache.ptr();
- const Vector3 *rp = baked_point_cache.ptr();
- const real_t *rt = baked_tilt_cache.ptr();
+ p_offset = CLAMP(p_offset, 0.0, get_baked_length()); // PathFollower implement wrapping logic.
- int start = 0;
- int end = count;
- int idx = (end + start) / 2;
- // Binary search to find baked points.
- while (start < idx) {
- real_t offset = baked_dist_cache[idx];
- if (p_offset <= offset) {
- end = idx;
- } else {
- start = idx;
- }
- idx = (end + start) / 2;
+ Curve3D::Interval interval = _find_interval(p_offset);
+ return _sample_baked(interval, p_cubic);
+}
+
+Transform3D Curve3D::sample_baked_with_rotation(real_t p_offset, bool p_cubic, bool p_apply_tilt) const {
+ if (baked_cache_dirty) {
+ _bake();
}
- if (idx == count - 1) {
- return p_apply_tilt ? r[idx].rotated((rp[idx] - rp[idx - 1]).normalized(), rt[idx]) : r[idx];
+ // Validate: Curve may not have baked points.
+ const int point_count = baked_point_cache.size();
+ ERR_FAIL_COND_V_MSG(point_count == 0, Transform3D(), "No points in Curve3D.");
+
+ if (point_count == 1) {
+ Transform3D t;
+ t.origin = baked_point_cache.get(0);
+ ERR_FAIL_V_MSG(t, "Only 1 point in Curve3D.");
}
- real_t offset_begin = baked_dist_cache[idx];
- real_t offset_end = baked_dist_cache[idx + 1];
+ p_offset = CLAMP(p_offset, 0.0, get_baked_length()); // PathFollower implement wrapping logic.
- real_t idx_interval = offset_end - offset_begin;
- ERR_FAIL_COND_V_MSG(p_offset < offset_begin || p_offset > offset_end, Vector3(0, 1, 0), "Couldn't find baked segment.");
+ // 0. Find interval for all sampling steps.
+ Curve3D::Interval interval = _find_interval(p_offset);
- real_t frac = (p_offset - offset_begin) / idx_interval;
+ // 1. Sample position.
+ Vector3 pos = _sample_baked(interval, p_cubic);
+
+ // 2. Sample rotation frame.
+ Basis frame = _sample_posture(interval, p_apply_tilt);
+
+ return Transform3D(frame, pos);
+}
+
+real_t Curve3D::sample_baked_tilt(real_t p_offset) const {
+ if (baked_cache_dirty) {
+ _bake();
+ }
- Vector3 forward = (rp[idx + 1] - rp[idx]).normalized();
- Vector3 up = r[idx];
- Vector3 up1 = r[idx + 1];
+ // Validate: Curve may not have baked tilts.
+ int pc = baked_tilt_cache.size();
+ ERR_FAIL_COND_V_MSG(pc == 0, 0, "No tilts in Curve3D.");
- if (p_apply_tilt) {
- up.rotate(forward, rt[idx]);
- up1.rotate(idx + 2 >= count ? forward : (rp[idx + 2] - rp[idx + 1]).normalized(), rt[idx + 1]);
+ if (pc == 1) {
+ return baked_tilt_cache.get(0);
}
- Vector3 axis = up.cross(up1);
+ p_offset = CLAMP(p_offset, 0.0, get_baked_length()); // PathFollower implement wrapping logic
- if (axis.length_squared() < CMP_EPSILON2) {
- axis = forward;
- } else {
- axis.normalize();
+ Curve3D::Interval interval = _find_interval(p_offset);
+ return _sample_baked_tilt(interval);
+}
+
+Vector3 Curve3D::sample_baked_up_vector(real_t p_offset, bool p_apply_tilt) const {
+ if (baked_cache_dirty) {
+ _bake();
+ }
+
+ // Validate: Curve may not have baked up vectors.
+ ERR_FAIL_COND_V_MSG(!up_vector_enabled, Vector3(0, 1, 0), "No up vectors in Curve3D.");
+
+ int count = baked_up_vector_cache.size();
+ if (count == 1) {
+ return baked_up_vector_cache.get(0);
}
- return up.rotated(axis, up.angle_to(up1) * frac);
+ p_offset = CLAMP(p_offset, 0.0, get_baked_length()); // PathFollower implement wrapping logic.
+
+ Curve3D::Interval interval = _find_interval(p_offset);
+ return _sample_posture(interval, p_apply_tilt).get_column(1);
}
PackedVector3Array Curve3D::get_baked_points() const {
@@ -2034,6 +2138,7 @@ void Curve3D::_bind_methods() {
ClassDB::bind_method(D_METHOD("get_baked_length"), &Curve3D::get_baked_length);
ClassDB::bind_method(D_METHOD("sample_baked", "offset", "cubic"), &Curve3D::sample_baked, DEFVAL(false));
+ ClassDB::bind_method(D_METHOD("sample_baked_with_rotation", "offset", "cubic", "apply_tilt"), &Curve3D::sample_baked_with_rotation, DEFVAL(false), DEFVAL(false));
ClassDB::bind_method(D_METHOD("sample_baked_up_vector", "offset", "apply_tilt"), &Curve3D::sample_baked_up_vector, DEFVAL(false));
ClassDB::bind_method(D_METHOD("get_baked_points"), &Curve3D::get_baked_points);
ClassDB::bind_method(D_METHOD("get_baked_tilts"), &Curve3D::get_baked_tilts);
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-15 04:10:18 +0000