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Cleaned up trigonometry.

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* Do one conversion to radians for sin and cos.
* Added atan2Deg.
* PathConstraint wasn't using SpineUtils.
* PointAttachment was using MathUtils.
This commit is contained in:
Nathan Sweet 2023-01-13 22:28:09 -04:00
parent 45c51b0c4f
commit 92164921a5
8 changed files with 95 additions and 86 deletions
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101
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/Bone.java
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@ -110,11 +110,13 @@ public class Bone implements Updatable {
Bone parent = this.parent;
if (parent == null) { // Root bone.
Skeleton skeleton = this.skeleton;
float rotationY = rotation + 90 + shearY, sx = skeleton.scaleX, sy = skeleton.scaleY;
a = cosDeg(rotation + shearX) * scaleX * sx;
b = cosDeg(rotationY) * scaleY * sx;
c = sinDeg(rotation + shearX) * scaleX * sy;
d = sinDeg(rotationY) * scaleY * sy;
float sx = skeleton.scaleX, sy = skeleton.scaleY;
float rx = (rotation + shearX) * degRad;
float ry = (rotation + 90 + shearY) * degRad;
a = cos(rx) * scaleX * sx;
b = cos(ry) * scaleY * sx;
c = sin(rx) * scaleX * sy;
d = sin(ry) * scaleY * sy;
worldX = x * sx + skeleton.x;
worldY = y * sy + skeleton.y;
return;
@ -126,11 +128,12 @@ public class Bone implements Updatable {
switch (data.transformMode) {
case normal: {
float rotationY = rotation + 90 + shearY;
float la = cosDeg(rotation + shearX) * scaleX;
float lb = cosDeg(rotationY) * scaleY;
float lc = sinDeg(rotation + shearX) * scaleX;
float ld = sinDeg(rotationY) * scaleY;
float rx = (rotation + shearX) * degRad;
float ry = (rotation + 90 + shearY) * degRad;
float la = cos(rx) * scaleX;
float lb = cos(ry) * scaleY;
float lc = sin(rx) * scaleX;
float ld = sin(ry) * scaleY;
a = pa * la + pb * lc;
b = pa * lb + pb * ld;
c = pc * la + pd * lc;
@ -138,11 +141,12 @@ public class Bone implements Updatable {
return;
}
case onlyTranslation: {
float rotationY = rotation + 90 + shearY;
a = cosDeg(rotation + shearX) * scaleX;
b = cosDeg(rotationY) * scaleY;
c = sinDeg(rotation + shearX) * scaleX;
d = sinDeg(rotationY) * scaleY;
float rx = (rotation + shearX) * degRad;
float ry = (rotation + 90 + shearY) * degRad;
a = cos(rx) * scaleX;
b = cos(ry) * scaleY;
c = sin(rx) * scaleX;
d = sin(ry) * scaleY;
break;
}
case noRotationOrReflection: {
@ -153,18 +157,18 @@ public class Bone implements Updatable {
pc /= skeleton.scaleY;
pb = pc * s;
pd = pa * s;
prx = atan2(pc, pa) * radDeg;
prx = atan2Deg(pc, pa);
} else {
pa = 0;
pc = 0;
prx = 90 - atan2(pd, pb) * radDeg;
prx = 90 - atan2Deg(pd, pb);
}
float rx = rotation + shearX - prx;
float ry = rotation + shearY - prx + 90;
float la = cosDeg(rx) * scaleX;
float lb = cosDeg(ry) * scaleY;
float lc = sinDeg(rx) * scaleX;
float ld = sinDeg(ry) * scaleY;
float rx = (rotation + shearX - prx) * degRad;
float ry = (rotation + shearY - prx + 90) * degRad;
float la = cos(rx) * scaleX;
float lb = cos(ry) * scaleY;
float lc = sin(rx) * scaleX;
float ld = sin(ry) * scaleY;
a = pa * la - pb * lc;
b = pa * lb - pb * ld;
c = pc * la + pd * lc;
@ -173,7 +177,8 @@ public class Bone implements Updatable {
}
case noScale:
case noScaleOrReflection:
float cos = cosDeg(rotation), sin = sinDeg(rotation);
rotation *= degRad;
float cos = cos(rotation), sin = sin(rotation);
float za = (pa * cos + pb * sin) / skeleton.scaleX;
float zc = (pc * cos + pd * sin) / skeleton.scaleY;
float s = (float)Math.sqrt(za * za + zc * zc);
@ -183,13 +188,15 @@ public class Bone implements Updatable {
s = (float)Math.sqrt(za * za + zc * zc);
if (data.transformMode == TransformMode.noScale
&& (pa * pd - pb * pc < 0) != (skeleton.scaleX < 0 != skeleton.scaleY < 0)) s = -s;
float r = PI / 2 + atan2(zc, za);
float zb = cos(r) * s;
float zd = sin(r) * s;
float la = cosDeg(shearX) * scaleX;
float lb = cosDeg(90 + shearY) * scaleY;
float lc = sinDeg(shearX) * scaleX;
float ld = sinDeg(90 + shearY) * scaleY;
rotation = PI / 2 + atan2(zc, za);
float zb = cos(rotation) * s;
float zd = sin(rotation) * s;
shearX *= degRad;
shearY = (90 + shearY) * degRad;
float la = cos(shearX) * scaleX;
float lb = cos(shearY) * scaleY;
float lc = sin(shearX) * scaleX;
float ld = sin(shearY) * scaleY;
a = za * la + zb * lc;
b = za * lb + zb * ld;
c = zc * la + zd * lc;
@ -398,11 +405,11 @@ public class Bone implements Updatable {
ax = worldX - skeleton.x;
ay = worldY - skeleton.y;
float a = this.a, b = this.b, c = this.c, d = this.d;
arotation = atan2(c, a) * radDeg;
arotation = atan2Deg(c, a);
ascaleX = (float)Math.sqrt(a * a + c * c);
ascaleY = (float)Math.sqrt(b * b + d * d);
ashearX = 0;
ashearY = atan2(a * b + c * d, a * d - b * c) * radDeg;
ashearY = atan2Deg(a * b + c * d, a * d - b * c);
return;
}
@ -434,7 +441,7 @@ public class Bone implements Updatable {
}
case noScale:
case noScaleOrReflection:
float cos = cosDeg(rotation), sin = sinDeg(rotation);
float r = rotation * degRad, cos = cos(r), sin = sin(r);
pa = (pa * cos + pb * sin) / skeleton.scaleX;
pc = (pc * cos + pd * sin) / skeleton.scaleY;
float s = (float)Math.sqrt(pa * pa + pc * pc);
@ -443,7 +450,7 @@ public class Bone implements Updatable {
pc *= s;
s = (float)Math.sqrt(pa * pa + pc * pc);
if (data.transformMode == TransformMode.noScale && pid < 0 != (skeleton.scaleX < 0 != skeleton.scaleY < 0)) s = -s;
float r = PI / 2 + atan2(pc, pa);
r = PI / 2 + atan2(pc, pa);
pb = cos(r) * s;
pd = sin(r) * s;
pid = 1 / (pa * pd - pb * pc);
@ -463,13 +470,13 @@ public class Bone implements Updatable {
if (ascaleX > 0.0001f) {
float det = ra * rd - rb * rc;
ascaleY = det / ascaleX;
ashearY = -atan2(ra * rb + rc * rd, det) * radDeg;
arotation = atan2(rc, ra) * radDeg;
ashearY = -atan2Deg(ra * rb + rc * rd, det);
arotation = atan2Deg(rc, ra);
} else {
ascaleX = 0;
ascaleY = (float)Math.sqrt(rb * rb + rd * rd);
ashearY = 0;
arotation = 90 - atan2(rd, rb) * radDeg;
arotation = 90 - atan2Deg(rd, rb);
}
}
@ -531,12 +538,12 @@ public class Bone implements Updatable {
/** The world rotation for the X axis, calculated using {@link #a} and {@link #c}. */
public float getWorldRotationX () {
return atan2(c, a) * radDeg;
return atan2Deg(c, a);
}
/** The world rotation for the Y axis, calculated using {@link #b} and {@link #d}. */
public float getWorldRotationY () {
return atan2(d, b) * radDeg;
return atan2Deg(d, b);
}
/** The magnitude (always positive) of the world scale X, calculated using {@link #a} and {@link #c}. */
@ -585,15 +592,16 @@ public class Bone implements Updatable {
/** Transforms a world rotation to a local rotation. */
public float worldToLocalRotation (float worldRotation) {
float sin = sinDeg(worldRotation), cos = cosDeg(worldRotation);
return atan2(a * sin - c * cos, d * cos - b * sin) * radDeg + rotation - shearX;
worldRotation *= degRad;
float sin = sin(worldRotation), cos = cos(worldRotation);
return atan2Deg(a * sin - c * cos, d * cos - b * sin) + rotation - shearX;
}
/** Transforms a local rotation to a world rotation. */
public float localToWorldRotation (float localRotation) {
localRotation -= rotation - shearX;
float sin = sinDeg(localRotation), cos = cosDeg(localRotation);
return atan2(cos * c + sin * d, cos * a + sin * b) * radDeg;
localRotation = (localRotation - rotation - shearX) * degRad;
float sin = sin(localRotation), cos = cos(localRotation);
return atan2Deg(cos * c + sin * d, cos * a + sin * b);
}
/** Rotates the world transform the specified amount.
@ -601,7 +609,8 @@ public class Bone implements Updatable {
* After changes are made to the world transform, {@link #updateAppliedTransform()} should be called and {@link #update()} will
* need to be called on any child bones, recursively. */
public void rotateWorld (float degrees) {
float cos = cosDeg(degrees), sin = sinDeg(degrees);
degrees *= degRad;
float sin = sin(degrees), cos = cos(degrees);
a = cos * a - sin * c;
b = cos * b - sin * d;
c = sin * a + cos * c;

4
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/IkConstraint.java
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@ -200,7 +200,7 @@ public class IkConstraint implements Updatable {
float sc = pc / bone.skeleton.scaleY;
pb = -sc * s * bone.skeleton.scaleX;
pd = sa * s * bone.skeleton.scaleY;
rotationIK += atan2(sc, sa) * radDeg;
rotationIK += atan2Deg(sc, sa);
// Fall through.
default:
float x = targetX - p.worldX, y = targetY - p.worldY;
@ -208,7 +208,7 @@ public class IkConstraint implements Updatable {
tx = (x * pd - y * pb) / d - bone.ax;
ty = (y * pa - x * pc) / d - bone.ay;
}
rotationIK += atan2(ty, tx) * radDeg;
rotationIK += atan2Deg(ty, tx);
if (bone.ascaleX < 0) rotationIK += 180;
if (rotationIK > 180)
rotationIK -= 360;

30
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/PathConstraint.java
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@ -203,11 +203,11 @@ public class PathConstraint implements Updatable {
else if (spaces[i + 1] < epsilon)
r = positions[p + 2];
else
r = (float)Math.atan2(dy, dx);
r -= (float)Math.atan2(c, a);
r = atan2(dy, dx);
r -= atan2(c, a);
if (tip) {
cos = (float)Math.cos(r);
sin = (float)Math.sin(r);
cos = cos(r);
sin = sin(r);
float length = bone.data.length;
boneX += (length * (cos * a - sin * c) - dx) * mixRotate;
boneY += (length * (sin * a + cos * c) - dy) * mixRotate;
@ -218,8 +218,8 @@ public class PathConstraint implements Updatable {
else if (r < -PI) //
r += PI2;
r *= mixRotate;
cos = (float)Math.cos(r);
sin = (float)Math.sin(r);
cos = cos(r);
sin = sin(r);
bone.a = cos * a - sin * c;
bone.b = cos * b - sin * d;
bone.c = sin * a + cos * c;
@ -465,16 +465,16 @@ public class PathConstraint implements Updatable {
}
private void addBeforePosition (float p, float[] temp, int i, float[] out, int o) {
float x1 = temp[i], y1 = temp[i + 1], dx = temp[i + 2] - x1, dy = temp[i + 3] - y1, r = (float)Math.atan2(dy, dx);
out[o] = x1 + p * (float)Math.cos(r);
out[o + 1] = y1 + p * (float)Math.sin(r);
float x1 = temp[i], y1 = temp[i + 1], dx = temp[i + 2] - x1, dy = temp[i + 3] - y1, r = atan2(dy, dx);
out[o] = x1 + p * cos(r);
out[o + 1] = y1 + p * sin(r);
out[o + 2] = r;
}
private void addAfterPosition (float p, float[] temp, int i, float[] out, int o) {
float x1 = temp[i + 2], y1 = temp[i + 3], dx = x1 - temp[i], dy = y1 - temp[i + 1], r = (float)Math.atan2(dy, dx);
out[o] = x1 + p * (float)Math.cos(r);
out[o + 1] = y1 + p * (float)Math.sin(r);
float x1 = temp[i + 2], y1 = temp[i + 3], dx = x1 - temp[i], dy = y1 - temp[i + 1], r = atan2(dy, dx);
out[o] = x1 + p * cos(r);
out[o + 1] = y1 + p * sin(r);
out[o + 2] = r;
}
@ -483,7 +483,7 @@ public class PathConstraint implements Updatable {
if (p < epsilon || Float.isNaN(p)) {
out[o] = x1;
out[o + 1] = y1;
out[o + 2] = (float)Math.atan2(cy1 - y1, cx1 - x1);
out[o + 2] = atan2(cy1 - y1, cx1 - x1);
return;
}
float tt = p * p, ttt = tt * p, u = 1 - p, uu = u * u, uuu = uu * u;
@ -493,9 +493,9 @@ public class PathConstraint implements Updatable {
out[o + 1] = y;
if (tangents) {
if (p < 0.001f)
out[o + 2] = (float)Math.atan2(cy1 - y1, cx1 - x1);
out[o + 2] = atan2(cy1 - y1, cx1 - x1);
else
out[o + 2] = (float)Math.atan2(y - (y1 * uu + cy1 * ut * 2 + cy2 * tt), x - (x1 * uu + cx1 * ut * 2 + cx2 * tt));
out[o + 2] = atan2(y - (y1 * uu + cy1 * ut * 2 + cy2 * tt), x - (x1 * uu + cx1 * ut * 2 + cx2 * tt));
}
}

2
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/PhysicsConstraint.java
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@ -371,7 +371,7 @@ public class PhysicsConstraint implements Updatable {
float s = (float)Math.sqrt(dx * dx + dy * dy) / length, r = atan2(dy, dx), sin = sin(r), cos = cos(r);
if (constraint.mix == 1) {
bone.updateWorldTransform(bone.ax, bone.ay,
atan2(bone.a * sin - bone.c * cos, bone.d * cos - bone.b * sin) * radDeg + bone.arotation - bone.ashearX,
atan2Deg(bone.a * sin - bone.c * cos, bone.d * cos - bone.b * sin) + bone.arotation - bone.ashearX,
bone.ascaleX * s, bone.ascaleY, bone.ashearX, bone.ashearY);
} else {
// BOZO

11
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/Skeleton.java
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@ -444,11 +444,12 @@ public class Skeleton {
rootBone.worldX = pa * x + pb * y + parent.worldX;
rootBone.worldY = pc * x + pd * y + parent.worldY;
float rotationY = rootBone.rotation + 90 + rootBone.shearY;
float la = cosDeg(rootBone.rotation + rootBone.shearX) * rootBone.scaleX;
float lb = cosDeg(rotationY) * rootBone.scaleY;
float lc = sinDeg(rootBone.rotation + rootBone.shearX) * rootBone.scaleX;
float ld = sinDeg(rotationY) * rootBone.scaleY;
float rx = (rootBone.rotation + rootBone.shearX) * degRad;
float ry = (rootBone.rotation + 90 + rootBone.shearY) * degRad;
float la = cos(rx) * rootBone.scaleX;
float lb = cos(ry) * rootBone.scaleY;
float lc = sin(rx) * rootBone.scaleX;
float ld = sin(ry) * rootBone.scaleY;
rootBone.a = (pa * la + pb * lc) * scaleX;
rootBone.b = (pa * lb + pb * ld) * scaleX;
rootBone.c = (pc * la + pd * lc) * scaleY;

6
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/attachments/PointAttachment.java
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@ -29,7 +29,7 @@
package com.esotericsoftware.spine.attachments;
import static com.badlogic.gdx.math.MathUtils.*;
import static com.esotericsoftware.spine.utils.SpineUtils.*;
import com.badlogic.gdx.graphics.Color;
import com.badlogic.gdx.math.Vector2;
@ -97,10 +97,10 @@ public class PointAttachment extends Attachment {
}
public float computeWorldRotation (Bone bone) {
float cos = cosDeg(rotation), sin = sinDeg(rotation);
float r = rotation * degRad, cos = cos(r), sin = sin(r);
float x = cos * bone.getA() + sin * bone.getB();
float y = cos * bone.getC() + sin * bone.getD();
return (float)Math.atan2(y, x) * radDeg;
return atan2Deg(y, x);
}
public PointAttachment copy () {

13
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/attachments/RegionAttachment.java
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@ -93,8 +93,7 @@ public class RegionAttachment extends Attachment implements HasTextureRegion {
return;
}
float width = getWidth();
float height = getHeight();
float width = getWidth(), height = getHeight();
float localX2 = width / 2;
float localY2 = height / 2;
float localX = -localX2;
@ -113,17 +112,13 @@ public class RegionAttachment extends Attachment implements HasTextureRegion {
localY2 -= (region.originalHeight - region.offsetY - region.packedHeight) / region.originalHeight * height;
}
}
float scaleX = getScaleX();
float scaleY = getScaleY();
float scaleX = getScaleX(), scaleY = getScaleY();
localX *= scaleX;
localY *= scaleY;
localX2 *= scaleX;
localY2 *= scaleY;
float rotation = getRotation();
float cos = (float)Math.cos(degRad * rotation);
float sin = (float)Math.sin(degRad * rotation);
float x = getX();
float y = getY();
float r = getRotation() * degRad, cos = cos(r), sin = sin(r);
float x = getX(), y = getY();
float localXCos = localX * cos + x;
float localXSin = localX * sin;
float localYCos = localY * cos + y;

14
spine-libgdx/spine-libgdx/src/com/esotericsoftware/spine/utils/SpineUtils.java
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@ -37,23 +37,27 @@ public class SpineUtils {
static public final float degreesToRadians = PI / 180;
static public final float degRad = degreesToRadians;
public static float cosDeg (float degrees) {
static public float cosDeg (float degrees) {
return (float)Math.cos(degrees * degRad);
}
public static float sinDeg (float degrees) {
static public float sinDeg (float degrees) {
return (float)Math.sin(degrees * degRad);
}
public static float cos (float radians) {
static public float cos (float radians) {
return (float)Math.cos(radians);
}
public static float sin (float radians) {
static public float sin (float radians) {
return (float)Math.sin(radians);
}
public static float atan2 (float y, float x) {
static public float atan2Deg (float y, float x) {
return (float)Math.atan2(y, x) * radDeg;
}
static public float atan2 (float y, float x) {
return (float)Math.atan2(y, x);
}