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| <li><div class="icon-class"></div><strong>quat</strong></li> |
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| <div class="content"> |
| <h2>Class |
| <strong>quat</strong></h2> |
| |
| <div class="doc"> |
| |
| </div> |
| <h3>Constructors</h3> |
| <div class="method"><h4 id="quat"> |
| <span class="show-code">Code</span> |
| new <strong>quat</strong>([a, b, c, d]) <a class="anchor-link" href="#quat" |
| title="Permalink to quat.quat">#</a></h4> |
| <div class="doc"> |
| <p>Constructs a new quaternion. Behaviour depends on the types of arguments:</p><ul><li><em>(<code>num</code> x,<code>num</code> y,<code>num</code> z,<code>num</code> w)</em> Raw values</li><li><em>(<a class="crossref" href="../VectorMath/vec3.html">vec3</a> axis,<code>num</code> angle)</em> Rotation of <code>angle</code> degrees around <a class="crossref" href="../VectorMath/quat.html#get:axis">axis</a></li><li><em>(<a class="crossref" href="../VectorMath/quat.html">quat</a> other)</em> Copy of other</li><li><em>(<a class="crossref" href="../VectorMath/mat3x3.html">mat3x3</a>)</em> Convert rotation matrix into quaternion</li></ul> |
| <pre class="source"> |
| quat([Dynamic a, Dynamic b, Dynamic c, Dynamic d]) { |
| x = 0.0; |
| y = 0.0; |
| z = 0.0; |
| w = 1.0; |
| |
| if (a is num && b is num && c is num && d is num) { |
| x = a; |
| y = b; |
| z = c; |
| w = d; |
| return; |
| } |
| |
| if (a is vec3 && b is num) { |
| setAxisAngle(a, b); |
| return; |
| } |
| |
| if (a is vec3) { |
| x = a.x; |
| y = a.y; |
| z = a.z; |
| w = 0.0; |
| return; |
| } |
| |
| if (a is quat) { |
| x = a._x; |
| y = a._y; |
| z = a._z; |
| w = a._w; |
| return; |
| } |
| |
| if (a is mat3x3) { |
| num trace = a.trace(); |
| List<num> temp = new List<num>(4); |
| if (trace > 0.0) { |
| num s = Math.sqrt(trace + 1.0); |
| temp[3]=(s * 0.5); |
| s = 0.5 / s; |
| |
| temp[0] = ((a[1].z - a[2].y) * s); |
| temp[1] = ((a[0].z - a[0].z) * s); |
| temp[2] = ((a[0].y - a[1].x) * s); |
| } else { |
| int i = a[0].x < a[1].y ? (a[1].y < a[2].z ? 2 : 1) : (a[0].x < a[2].z ? 2 : 0); |
| int j = (i + 1) % 3; |
| int k = (i + 2) % 3; |
| |
| num s = Math.sqrt(a[i][i] - a[j][j] - a[k][k] + 1.0); |
| temp[i] = s * 0.5; |
| s = 0.5 / s; |
| |
| temp[3] = (a[k][j] - a[j][k]) * s; |
| temp[j] = (a[j][i] + a[i][j]) * s; |
| temp[k] = (a[k][i] + a[i][k]) * s; |
| } |
| x = temp[0]; |
| y = temp[1]; |
| z = temp[2]; |
| w = temp[3]; |
| } |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="quat"> |
| <span class="show-code">Code</span> |
| new <strong>quat</strong>.dq(<a href="../VectorMath/quat.html">quat</a> q, <a href="../VectorMath/vec3.html">vec3</a> omega) <a class="anchor-link" href="#quat" |
| title="Permalink to quat.quat">#</a></h4> |
| <div class="doc"> |
| <p>Generate the time derivative of |
| <span class="param">q</span> with angular velocity |
| <span class="param">omega</span></p> |
| <pre class="source"> |
| quat.dq(quat q, vec3 omega) { |
| x = omega.x * q.w + omega.y * q.z - omega.z * q.y; |
| y = omega.y * q.w + omega.z * q.x - omega.x * q.z; |
| z = omega.z * q.w + omega.x * q.y - omega.y * q.x; |
| w = -omega.x * q.x - omega.y * q.y - omega.z * q.z; |
| x *= 0.5; |
| y *= 0.5; |
| z *= 0.5; |
| w *= 0.5; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="quat"> |
| <span class="show-code">Code</span> |
| new <strong>quat</strong>.random() <a class="anchor-link" href="#quat" |
| title="Permalink to quat.quat">#</a></h4> |
| <div class="doc"> |
| <p>Generate a random rotation</p> |
| <pre class="source"> |
| quat.random() { |
| // From: "Uniform Random Rotations", Ken Shoemake, Graphics Gems III, |
| // pg. 124-132 |
| num x0 = Math.random(); |
| num r1 = Math.sqrt(1.0 - x0); |
| num r2 = Math.sqrt(x0); |
| num t1 = Math.PI*2.0 * Math.random(); |
| num t2 = Math.PI*2.0 * Math.random(); |
| num c1 = Math.cos(t1); |
| num s1 = Math.sin(t1); |
| num c2 = Math.cos(t2); |
| num s2 = Math.sin(t2); |
| x = s1 * r1; |
| y = c1 * r1; |
| z = s2 * r2; |
| w = c2 * r2; |
| } |
| </pre> |
| </div> |
| </div> |
| <h3>Methods</h3> |
| <div class="method"><h4 id="setAxisAngle"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/void.html">void</a> <strong>setAxisAngle</strong>(<a href="../VectorMath/vec3.html">vec3</a> axis, <a href="../dart_core/num.html">num</a> radians) <a class="anchor-link" href="#setAxisAngle" |
| title="Permalink to quat.setAxisAngle">#</a></h4> |
| <div class="doc"> |
| <p>Reset quaternion with rotation of |
| <span class="param">radians</span> around |
| <span class="param">axis</span></p> |
| <pre class="source"> |
| void setAxisAngle(vec3 axis, num radians) { |
| num len = axis.length; |
| if (len == 0.0) { |
| return; |
| } |
| num halfSin = sin(radians * 0.5) / len; |
| x = axis.x * halfSin; |
| y = axis.y * halfSin; |
| z = axis.z * halfSin; |
| w = cos(radians * 0.5); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="setEuler"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/void.html">void</a> <strong>setEuler</strong>(<a href="../dart_core/num.html">num</a> yaw, <a href="../dart_core/num.html">num</a> pitch, <a href="../dart_core/num.html">num</a> roll) <a class="anchor-link" href="#setEuler" |
| title="Permalink to quat.setEuler">#</a></h4> |
| <div class="doc"> |
| <p>Reset quaternion with rotation of |
| <span class="param">yaw</span>, |
| <span class="param">pitch</span> and |
| <span class="param">roll</span></p> |
| <pre class="source"> |
| void setEuler(num yaw, num pitch, num roll) { |
| num halfYaw = yaw * 0.5; |
| num halfPitch = pitch * 0.5; |
| num halfRoll = roll * 0.5; |
| num cosYaw = halfYaw; |
| num sinYaw = halfYaw; |
| num cosPitch = halfPitch; |
| num sinPitch = halfPitch; |
| num cosRoll = halfRoll; |
| num sinRoll = halfRoll; |
| x = cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw; |
| y = cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw; |
| z = sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw; |
| w = cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="normalize"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>normalize</strong>() <a class="anchor-link" href="#normalize" |
| title="Permalink to quat.normalize">#</a></h4> |
| <div class="doc"> |
| <p>Quaternion becomes normalized</p> |
| <pre class="source"> |
| quat normalize() { |
| num l = length; |
| if (l == 0.0) { |
| return this; |
| } |
| x /= l; |
| y /= l; |
| z /= l; |
| w /= l; |
| return this; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="conjugate"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>conjugate</strong>() <a class="anchor-link" href="#conjugate" |
| title="Permalink to quat.conjugate">#</a></h4> |
| <div class="doc"> |
| <p>Quaternion becomes conjugate of itself</p> |
| <pre class="source"> |
| quat conjugate() { |
| x = -x; |
| y = -y; |
| z = -z; |
| w = w; |
| return this; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="inverse"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>inverse</strong>() <a class="anchor-link" href="#inverse" |
| title="Permalink to quat.inverse">#</a></h4> |
| <div class="doc"> |
| <p>Quaternion becomes inverse of itself</p> |
| <pre class="source"> |
| quat inverse() { |
| x = -x; |
| y = -y; |
| z = -z; |
| w = w; |
| return this; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="normalized"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>normalized</strong>() <a class="anchor-link" href="#normalized" |
| title="Permalink to quat.normalized">#</a></h4> |
| <div class="doc"> |
| <p>Returns normalized copy of quaternion</p> |
| <pre class="source"> |
| quat normalized() { |
| return (new quat(this)).normalize(); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="conjugated"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>conjugated</strong>() <a class="anchor-link" href="#conjugated" |
| title="Permalink to quat.conjugated">#</a></h4> |
| <div class="doc"> |
| <p>Returns conjugated copy of quaternion</p> |
| <pre class="source"> |
| quat conjugated() { |
| return (new quat(this)).conjugate(); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="inverted"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>inverted</strong>() <a class="anchor-link" href="#inverted" |
| title="Permalink to quat.inverted">#</a></h4> |
| <div class="doc"> |
| <p>Returns inverted copy of quaternion</p> |
| <pre class="source"> |
| quat inverted() { |
| return (new quat(this)).inverse(); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="get:radians"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>get radians</strong>() <a class="anchor-link" href="#get:radians" |
| title="Permalink to quat.get radians">#</a></h4> |
| <div class="doc"> |
| <p>Radians of rotation</p> |
| <pre class="source"> |
| num get radians() { |
| return 2.0 * acos(w); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="get:axis"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/vec3.html">vec3</a> <strong>get axis</strong>() <a class="anchor-link" href="#get:axis" |
| title="Permalink to quat.get axis">#</a></h4> |
| <div class="doc"> |
| <p>Axis of rotation</p> |
| <pre class="source"> |
| vec3 get axis() { |
| num divisor = 1.0 - (w*w); |
| return new vec3(x / divisor, y / divisor, z / divisor); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="get:length2"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>get length2</strong>() <a class="anchor-link" href="#get:length2" |
| title="Permalink to quat.get length2">#</a></h4> |
| <div class="doc"> |
| <p>Squared length</p> |
| <pre class="source"> |
| num get length2() { |
| return (x*x) + (y*y) + (z*z) + (w*w); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="get:length"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>get length</strong>() <a class="anchor-link" href="#get:length" |
| title="Permalink to quat.get length">#</a></h4> |
| <div class="doc"> |
| <p>Length</p> |
| <pre class="source"> |
| num get length() { |
| return sqrt(length2); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="rotate"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/vec3.html">vec3</a> <strong>rotate</strong>(<a href="../VectorMath/vec3.html">vec3</a> v) <a class="anchor-link" href="#rotate" |
| title="Permalink to quat.rotate">#</a></h4> |
| <div class="doc"> |
| <p>Returns v rotated by quaternion</p> |
| <pre class="source"> |
| vec3 rotate(vec3 v) { |
| quat v_as_quat = new quat(v); |
| quat this_inverted = inverse(); |
| quat result = this * v_as_quat * this_inverted; |
| vec3 o = new vec3(result.x, result.y, result.z); |
| return o; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id=":div"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>operator /</strong>(<a href="../dart_core/num.html">num</a> scale) <a class="anchor-link" href="#:div" |
| title="Permalink to quat.operator /">#</a></h4> |
| <div class="doc"> |
| <p>Returns copy of quaternion divided by |
| <span class="param">scale</span></p> |
| <pre class="source"> |
| quat operator/(num scale) { |
| return new quat(x / scale, y / scale, z / scale, w / scale); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id=":mul"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>operator *</strong>(other) <a class="anchor-link" href="#:mul" |
| title="Permalink to quat.operator *">#</a></h4> |
| <div class="doc"> |
| <p>Returns copy of quaternion multiplied by <code>scale</code> |
| Returns copy of quaternion rotated by <code>otherQuat</code></p> |
| <pre class="source"> |
| quat operator*(Dynamic other) { |
| if (other is num) { |
| return new quat(x * other, y * other, z * other, w * other); |
| } |
| if (other is quat) { |
| return new quat(w * other.x + x * other.w + y * other.z - z * other.y, |
| w * other.y + y * other.w + z * other.x - x * other.z, |
| w * other.z + z * other.w + x * other.y - y * other.x, |
| w * other.w - x * other.x - y * other.y - z * other.z); |
| } |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id=":add"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>operator +</strong>(<a href="../VectorMath/quat.html">quat</a> other) <a class="anchor-link" href="#:add" |
| title="Permalink to quat.operator +">#</a></h4> |
| <div class="doc"> |
| <p>Returns copy of quaternion - |
| <span class="param">other</span></p> |
| <pre class="source"> |
| quat operator+(quat other) { |
| return new quat(x + other.x, y + other.y, z + other.z, w + other.w); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id=":sub"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>operator -</strong>(<a href="../VectorMath/quat.html">quat</a> other) <a class="anchor-link" href="#:sub" |
| title="Permalink to quat.operator -">#</a></h4> |
| <div class="doc"> |
| <p>Returns copy of quaternion + |
| <span class="param">other</span></p> |
| <pre class="source"> |
| quat operator-(quat other) { |
| return new quat(x - other.x, y - other.y, z - other.z, w - other.w); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id=":negate"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/quat.html">quat</a> <strong>operator negate</strong>() <a class="anchor-link" href="#:negate" |
| title="Permalink to quat.operator negate">#</a></h4> |
| <div class="doc"> |
| <p>Returns negated copy of quaternion</p> |
| <pre class="source"> |
| quat operator negate() { |
| return new quat(-x, -y, -z, -w); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id=":index"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>operator []</strong>(<a href="../dart_core/int.html">int</a> i) <a class="anchor-link" href="#:index" |
| title="Permalink to quat.operator []">#</a></h4> |
| <div class="doc"> |
| <p>Treats quaternion as an array and returns <a class="crossref" href="../VectorMath/quat.html#x">x</a>,<a class="crossref" href="../VectorMath/quat.html#y">y</a>,<a class="crossref" href="../VectorMath/quat.html#z">z</a>, or <a class="crossref" href="../VectorMath/quat.html#w">w</a></p> |
| <pre class="source"> |
| num operator[](int i) { |
| assert(i >= 0 && i < 4); |
| switch (i) { |
| case 0: return x; break; |
| case 1: return y; break; |
| case 2: return z; break; |
| case 3: return w; break; |
| } |
| return 0.0; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id=":setindex"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>operator []=</strong>(<a href="../dart_core/int.html">int</a> i, <a href="../dart_core/num.html">num</a> arg) <a class="anchor-link" href="#:setindex" |
| title="Permalink to quat.operator []=">#</a></h4> |
| <div class="doc"> |
| <p>Treats quaternion as an array and assigns <a class="crossref" href="../VectorMath/quat.html#x">x</a>,<a class="crossref" href="../VectorMath/quat.html#y">y</a>,<a class="crossref" href="../VectorMath/quat.html#z">z</a>, or <a class="crossref" href="../VectorMath/quat.html#w">w</a> the value of |
| <span class="param">arg</span></p> |
| <pre class="source"> |
| num operator[]=(int i, num arg) { |
| assert(i >= 0 && i < 4); |
| switch (i) { |
| case 0: x = arg; return x; break; |
| case 1: y = arg; return y; break; |
| case 2: z = arg; return z; break; |
| case 3: x = arg; return w; break; |
| } |
| return 0.0; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="asRotationMatrix"> |
| <span class="show-code">Code</span> |
| <a href="../VectorMath/mat3x3.html">mat3x3</a> <strong>asRotationMatrix</strong>() <a class="anchor-link" href="#asRotationMatrix" |
| title="Permalink to quat.asRotationMatrix">#</a></h4> |
| <div class="doc"> |
| <p>Converts quaternion into rotation matrix (<a class="crossref" href="../VectorMath/mat3x3.html">mat3x3</a>)</p> |
| <pre class="source"> |
| mat3x3 asRotationMatrix() { |
| num d = length2; |
| assert(d != 0.0); |
| num s = 2.0 / d; |
| num xs = x * s; |
| num ys = y * s; |
| num zs = z * s; |
| num wx = w * xs; |
| num wy = w * ys; |
| num wz = w * zs; |
| num xx = x * xs; |
| num xy = x * ys; |
| num xz = x * zs; |
| num yy = y * ys; |
| num yz = y * zs; |
| num zz = z * zs; |
| |
| return new mat3x3(1.0 - (yy + zz), xy + wz, xz - wy, // column 0 |
| xy - wz, 1.0 - (xx + zz), yz + wx, // column 1 |
| xz + wy, yz - wx, 1.0 - (xx + yy) // column 2 |
| ); |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="toString"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/String.html">String</a> <strong>toString</strong>() <a class="anchor-link" href="#toString" |
| title="Permalink to quat.toString">#</a></h4> |
| <div class="doc"> |
| <p>Returns a printable string</p> |
| <pre class="source"> |
| String toString() { |
| return '$x, $y, $z @ $w'; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="relativeError"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>relativeError</strong>(<a href="../VectorMath/quat.html">quat</a> correct) <a class="anchor-link" href="#relativeError" |
| title="Permalink to quat.relativeError">#</a></h4> |
| <div class="doc"> |
| <p>Returns relative error between this quaternion and |
| <span class="param">correct</span></p> |
| <pre class="source"> |
| num relativeError(quat correct) { |
| num this_norm = length; |
| num correct_norm = correct.length; |
| num norm_diff = (this_norm - correct_norm).abs(); |
| return norm_diff/correct_norm; |
| } |
| </pre> |
| </div> |
| </div> |
| <div class="method"><h4 id="absoluteError"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>absoluteError</strong>(<a href="../VectorMath/quat.html">quat</a> correct) <a class="anchor-link" href="#absoluteError" |
| title="Permalink to quat.absoluteError">#</a></h4> |
| <div class="doc"> |
| <p>Returns absolute error between this quaternion and |
| <span class="param">correct</span></p> |
| <pre class="source"> |
| num absoluteError(quat correct) { |
| num this_norm = length; |
| num correct_norm = correct.length; |
| num norm_diff = (this_norm - correct_norm).abs(); |
| return norm_diff; |
| } |
| </pre> |
| </div> |
| </div> |
| <h3>Fields</h3> |
| <div class="field"><h4 id="x"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>x</strong> <a class="anchor-link" |
| href="#x" |
| title="Permalink to quat.x">#</a> |
| </h4> |
| <div class="doc"> |
| |
| <pre class="source"> |
| num x; |
| </pre> |
| </div> |
| </div> |
| <div class="field"><h4 id="y"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>y</strong> <a class="anchor-link" |
| href="#y" |
| title="Permalink to quat.y">#</a> |
| </h4> |
| <div class="doc"> |
| |
| <pre class="source"> |
| num y; |
| </pre> |
| </div> |
| </div> |
| <div class="field"><h4 id="z"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>z</strong> <a class="anchor-link" |
| href="#z" |
| title="Permalink to quat.z">#</a> |
| </h4> |
| <div class="doc"> |
| |
| <pre class="source"> |
| num z; |
| </pre> |
| </div> |
| </div> |
| <div class="field"><h4 id="w"> |
| <span class="show-code">Code</span> |
| <a href="../dart_core/num.html">num</a> <strong>w</strong> <a class="anchor-link" |
| href="#w" |
| title="Permalink to quat.w">#</a> |
| </h4> |
| <div class="doc"> |
| |
| <pre class="source"> |
| num w; |
| </pre> |
| </div> |
| </div> |
| </div> |
| <div class="clear"></div> |
| </div> |
| <div class="footer"></div> |
| </body></html> |
| |
