Merge pull request #852 from aaronfranke/math
Rémi Verschelde
GitHub
commit
aaee30e5c5
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@ -28,8 +28,8 @@
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#ifndef GODOT_MATH_H
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#define GODOT_MATH_H
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#ifndef GODOT_MATH_HPP
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#define GODOT_MATH_HPP
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#include <godot_cpp/core/defs.hpp>
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@ -113,7 +113,7 @@ inline float fposmod(float p_x, float p_y) {
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if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
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value += p_y;
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}
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value += 0.0;
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value += 0.0f;
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return value;
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}
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@ -122,7 +122,7 @@ inline float fposmodp(float p_x, float p_y) {
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if (value < 0) {
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value += p_y;
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}
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value += 0.0;
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value += 0.0f;
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return value;
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}
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inline double fposmodp(double p_x, double p_y) {
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@ -134,6 +134,14 @@ inline double fposmodp(double p_x, double p_y) {
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return value;
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}
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inline int64_t posmod(int64_t p_x, int64_t p_y) {
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int64_t value = p_x % p_y;
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if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
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value += p_y;
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}
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return value;
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}
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inline double floor(double p_x) {
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return ::floor(p_x);
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}
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@ -280,17 +288,126 @@ inline float lerp_angle(float p_from, float p_to, float p_weight) {
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inline double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) {
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return 0.5 *
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((p_from * 2.0) +
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(-p_pre + p_to) * p_weight +
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(2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) +
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(-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight));
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((p_from * 2.0) +
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(-p_pre + p_to) * p_weight +
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(2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) +
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(-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight));
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}
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inline float cubic_interpolate(float p_from, float p_to, float p_pre, float p_post, float p_weight) {
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return 0.5f *
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((p_from * 2.0f) +
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(-p_pre + p_to) * p_weight +
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(2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) +
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(-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight));
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((p_from * 2.0f) +
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(-p_pre + p_to) * p_weight +
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(2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) +
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(-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight));
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}
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inline double cubic_interpolate_angle(double p_from, double p_to, double p_pre, double p_post, double p_weight) {
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double from_rot = fmod(p_from, Math_TAU);
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double pre_diff = fmod(p_pre - from_rot, Math_TAU);
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double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff;
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double to_diff = fmod(p_to - from_rot, Math_TAU);
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double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff;
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double post_diff = fmod(p_post - to_rot, Math_TAU);
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double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff;
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return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight);
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}
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inline float cubic_interpolate_angle(float p_from, float p_to, float p_pre, float p_post, float p_weight) {
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float from_rot = fmod(p_from, (float)Math_TAU);
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float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU);
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float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff;
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float to_diff = fmod(p_to - from_rot, (float)Math_TAU);
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float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff;
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float post_diff = fmod(p_post - to_rot, (float)Math_TAU);
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float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff;
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return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight);
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}
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inline double cubic_interpolate_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight,
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double p_to_t, double p_pre_t, double p_post_t) {
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/* Barry-Goldman method */
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double t = Math::lerp(0.0, p_to_t, p_weight);
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double a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0 : (t - p_pre_t) / -p_pre_t);
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double a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5 : t / p_to_t);
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double a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0 : (t - p_to_t) / (p_post_t - p_to_t));
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double b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0 : (t - p_pre_t) / (p_to_t - p_pre_t));
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double b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0 : t / p_post_t);
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return Math::lerp(b1, b2, p_to_t == 0 ? 0.5 : t / p_to_t);
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}
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inline float cubic_interpolate_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight,
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float p_to_t, float p_pre_t, float p_post_t) {
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/* Barry-Goldman method */
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float t = Math::lerp(0.0f, p_to_t, p_weight);
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float a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0f : (t - p_pre_t) / -p_pre_t);
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float a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5f : t / p_to_t);
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float a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0f : (t - p_to_t) / (p_post_t - p_to_t));
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float b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0f : (t - p_pre_t) / (p_to_t - p_pre_t));
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float b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0f : t / p_post_t);
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return Math::lerp(b1, b2, p_to_t == 0 ? 0.5f : t / p_to_t);
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}
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inline double cubic_interpolate_angle_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight,
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double p_to_t, double p_pre_t, double p_post_t) {
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double from_rot = fmod(p_from, Math_TAU);
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double pre_diff = fmod(p_pre - from_rot, Math_TAU);
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double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff;
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double to_diff = fmod(p_to - from_rot, Math_TAU);
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double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff;
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double post_diff = fmod(p_post - to_rot, Math_TAU);
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double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff;
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return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t);
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}
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inline float cubic_interpolate_angle_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight,
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float p_to_t, float p_pre_t, float p_post_t) {
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float from_rot = fmod(p_from, (float)Math_TAU);
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float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU);
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float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff;
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float to_diff = fmod(p_to - from_rot, (float)Math_TAU);
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float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff;
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float post_diff = fmod(p_post - to_rot, (float)Math_TAU);
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float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff;
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return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t);
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}
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inline double bezier_interpolate(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) {
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/* Formula from Wikipedia article on Bezier curves. */
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double omt = (1.0 - p_t);
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double omt2 = omt * omt;
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double omt3 = omt2 * omt;
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double t2 = p_t * p_t;
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double t3 = t2 * p_t;
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return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
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}
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inline float bezier_interpolate(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) {
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/* Formula from Wikipedia article on Bezier curves. */
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float omt = (1.0f - p_t);
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float omt2 = omt * omt;
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float omt3 = omt2 * omt;
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float t2 = p_t * p_t;
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float t3 = t2 * p_t;
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return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3;
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}
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template <typename T>
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@ -345,10 +462,10 @@ inline float inverse_lerp(float p_from, float p_to, float p_value) {
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return (p_value - p_from) / (p_to - p_from);
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}
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inline double range_lerp(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) {
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inline double remap(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) {
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return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
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}
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inline float range_lerp(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) {
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inline float remap(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) {
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return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
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}
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@ -368,30 +485,56 @@ inline bool is_inf(double p_val) {
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return std::isinf(p_val);
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}
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inline bool is_equal_approx(real_t a, real_t b) {
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inline bool is_equal_approx(float a, float b) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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real_t tolerance = CMP_EPSILON * std::abs(a);
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float tolerance = (float)CMP_EPSILON * abs(a);
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if (tolerance < (float)CMP_EPSILON) {
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tolerance = (float)CMP_EPSILON;
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}
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return abs(a - b) < tolerance;
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}
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inline bool is_equal_approx(float a, float b, float tolerance) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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return abs(a - b) < tolerance;
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}
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inline bool is_zero_approx(float s) {
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return abs(s) < (float)CMP_EPSILON;
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}
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inline bool is_equal_approx(double a, double b) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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double tolerance = CMP_EPSILON * abs(a);
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if (tolerance < CMP_EPSILON) {
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tolerance = CMP_EPSILON;
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}
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return std::abs(a - b) < tolerance;
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return abs(a - b) < tolerance;
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}
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inline bool is_equal_approx(real_t a, real_t b, real_t tolerance) {
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inline bool is_equal_approx(double a, double b, double tolerance) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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return std::abs(a - b) < tolerance;
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return abs(a - b) < tolerance;
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}
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inline bool is_zero_approx(real_t s) {
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return std::abs(s) < CMP_EPSILON;
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inline bool is_zero_approx(double s) {
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return abs(s) < CMP_EPSILON;
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}
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inline double smoothstep(double p_from, double p_to, double p_weight) {
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@ -448,17 +591,20 @@ inline float wrapf(real_t value, real_t min, real_t max) {
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return is_zero_approx(range) ? min : value - (range * floor((value - min) / range));
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}
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inline float stepify(float p_value, float p_step) {
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if (p_step != 0) {
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p_value = floor(p_value / p_step + 0.5f) * p_step;
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}
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return p_value;
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inline float fract(float value) {
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return value - floor(value);
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}
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inline double stepify(double p_value, double p_step) {
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if (p_step != 0) {
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p_value = floor(p_value / p_step + 0.5) * p_step;
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}
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return p_value;
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inline double fract(double value) {
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return value - floor(value);
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}
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inline float pingpong(float value, float length) {
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return (length != 0.0f) ? abs(fract((value - length) / (length * 2.0f)) * length * 2.0f - length) : 0.0f;
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}
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inline double pingpong(double value, double length) {
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return (length != 0.0) ? abs(fract((value - length) / (length * 2.0)) * length * 2.0 - length) : 0.0;
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}
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inline unsigned int next_power_of_2(unsigned int x) {
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@ -506,7 +652,25 @@ inline double snapped(double p_value, double p_step) {
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return p_value;
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}
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inline float snap_scalar(float p_offset, float p_step, float p_target) {
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return p_step != 0 ? Math::snapped(p_target - p_offset, p_step) + p_offset : p_target;
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}
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inline float snap_scalar_separation(float p_offset, float p_step, float p_target, float p_separation) {
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if (p_step != 0) {
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float a = Math::snapped(p_target - p_offset, p_step + p_separation) + p_offset;
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float b = a;
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if (p_target >= 0) {
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b -= p_separation;
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} else {
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b += p_step;
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}
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return (Math::abs(p_target - a) < Math::abs(p_target - b)) ? a : b;
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}
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return p_target;
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}
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} // namespace Math
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} // namespace godot
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#endif // GODOT_MATH_H
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#endif // GODOT_MATH_HPP
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@ -110,7 +110,7 @@ bool Basis::is_diagonal() const {
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}
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bool Basis::is_rotation() const {
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return Math::is_equal_approx(determinant(), 1, UNIT_EPSILON) && is_orthogonal();
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return Math::is_equal_approx(determinant(), (real_t)1, (real_t)UNIT_EPSILON) && is_orthogonal();
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}
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#ifdef MATH_CHECKS
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@ -86,7 +86,7 @@ Quaternion Quaternion::normalized() const {
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}
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bool Quaternion::is_normalized() const {
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return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); //use less epsilon
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return Math::is_equal_approx(length_squared(), (real_t)1.0, (real_t)UNIT_EPSILON); //use less epsilon
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}
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Quaternion Quaternion::inverse() const {
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