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https://github.com/BelfrySCAD/BOSL2.git
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Changes in Q_Angle computation and formatting
This commit is contained in:
RonaldoCMP
parent
fd0e74ac97
commit
8129176171
1 changed files with 153 additions and 156 deletions
309
quaternions.scad
309
quaternions.scad
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@ -47,11 +47,11 @@ function Q_is_quat(q) = is_vector(q,4) && ! approx(norm(q),0) ;
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// ax = Vector of axis of rotation.
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// ang = Number of degrees to rotate around the axis counter-clockwise, when facing the origin.
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function Quat(ax=[0,0,1], ang=0) =
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assert( is_vector(ax,3) && is_num(0*ang), "Invalid input")
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let( n = norm(ax) )
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approx(n,0)
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? _Quat([0,0,0], sin(ang/2), cos(ang/2))
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: _Quat(ax/n, sin(ang/2), cos(ang/2));
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assert( is_vector(ax,3) && is_finite(ang), "Invalid input")
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let( n = norm(ax) )
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approx(n,0)
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? _Quat([0,0,0], sin(ang/2), cos(ang/2))
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: _Quat(ax/n, sin(ang/2), cos(ang/2));
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// Function: QuatX()
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@ -61,8 +61,8 @@ function Quat(ax=[0,0,1], ang=0) =
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// Arguments:
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// a = Number of degrees to rotate around the axis counter-clockwise, when facing the origin.
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function QuatX(a=0) =
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assert( is_num(0*a), "Invalid angle" )
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Quat([1,0,0],a);
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assert( is_finite(a), "Invalid angle" )
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Quat([1,0,0],a);
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// Function: QuatY()
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@ -72,8 +72,8 @@ function QuatX(a=0) =
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// Arguments:
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// a = Number of degrees to rotate around the axis counter-clockwise, when facing the origin.
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function QuatY(a=0) =
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assert( is_num(0*a), "Invalid angle" )
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Quat([0,1,0],a);
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assert( is_finite(a), "Invalid angle" )
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Quat([0,1,0],a);
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// Function: QuatZ()
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@ -83,8 +83,8 @@ function QuatY(a=0) =
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// Arguments:
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// a = Number of degrees to rotate around the axis counter-clockwise, when facing the origin.
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function QuatZ(a=0) =
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assert( is_num(0*a), "Invalid angle" )
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Quat([0,0,1],a);
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assert( is_finite(a), "Invalid angle" )
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Quat([0,0,1],a);
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// Function: QuatXYZ()
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@ -95,11 +95,11 @@ function QuatZ(a=0) =
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// Arguments:
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// a = The triplet of rotation angles, [X,Y,Z]
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function QuatXYZ(a=[0,0,0]) =
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assert( is_vector(a,3), "Invalid angles")
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assert( is_vector(a,3), "Invalid angles")
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let(
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qx = QuatX(a[0]),
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qy = QuatY(a[1]),
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qz = QuatZ(a[2])
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qx = QuatX(a[0]),
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qy = QuatY(a[1]),
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qz = QuatZ(a[2])
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)
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Q_Mul(qz, Q_Mul(qy, qx));
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@ -111,14 +111,14 @@ function QuatXYZ(a=[0,0,0]) =
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// Returns the normalized quaternion that rotates the non zero 3D vector v1
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// to the non zero 3D vector v2.
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function Q_From_to(v1, v2) =
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assert( is_vector(v1,3) && is_vector(v2,3)
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&& ! approx(norm(v1),0) && ! approx(norm(v2),0)
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, "Invalid vector(s)")
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let( ax = cross(v1,v2),
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n = norm(ax) )
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approx(n, 0)
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? v1*v2>0 ? Q_Ident() : Quat([ v1.y, -v1.x, 0], 180)
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: Quat(ax, atan2( n , v1*v2 ));
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assert( is_vector(v1,3) && is_vector(v2,3)
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&& ! approx(norm(v1),0) && ! approx(norm(v2),0)
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, "Invalid vector(s)")
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let( ax = cross(v1,v2),
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n = norm(ax) )
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approx(n, 0)
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? v1*v2>0 ? Q_Ident() : Quat([ v1.y, -v1.x, 0], 180)
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: Quat(ax, atan2( n , v1*v2 ));
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// Function: Q_Ident()
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@ -133,8 +133,8 @@ function Q_Ident() = [0, 0, 0, 1];
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// Adds a scalar value `s` to the W part of a quaternion `q`.
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// The returned quaternion is usually not normalized.
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function Q_Add_S(q, s) =
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assert( is_num(0*s), "Invalid scalar" )
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q+[0,0,0,s];
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assert( is_finite(s), "Invalid scalar" )
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q+[0,0,0,s];
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// Function: Q_Sub_S()
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@ -144,8 +144,8 @@ function Q_Add_S(q, s) =
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// Subtracts a scalar value `s` from the W part of a quaternion `q`.
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// The returned quaternion is usually not normalized.
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function Q_Sub_S(q, s) =
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assert( is_num(0*s), "Invalid scalar" )
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q-[0,0,0,s];
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assert( is_finite(s), "Invalid scalar" )
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q-[0,0,0,s];
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// Function: Q_Mul_S()
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@ -155,8 +155,8 @@ function Q_Sub_S(q, s) =
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// Multiplies each part of a quaternion `q` by a scalar value `s`.
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// The returned quaternion is usually not normalized.
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function Q_Mul_S(q, s) =
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assert( is_num(0*s), "Invalid scalar" )
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q*s;
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assert( is_finite(s), "Invalid scalar" )
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q*s;
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// Function: Q_Div_S()
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@ -166,8 +166,8 @@ function Q_Mul_S(q, s) =
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// Divides each part of a quaternion `q` by a scalar value `s`.
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// The returned quaternion is usually not normalized.
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function Q_Div_S(q, s) =
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assert( is_num(0*s) && ! approx(s,0) , "Invalid scalar" )
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q/s;
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assert( is_finite(s) && ! approx(s,0) , "Invalid scalar" )
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q/s;
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// Function: Q_Add()
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@ -177,9 +177,9 @@ function Q_Div_S(q, s) =
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// Adds each part of two quaternions together.
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// The returned quaternion is usually not normalized.
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function Q_Add(a, b) =
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assert( Q_is_quat(a) && Q_is_quat(a), "Invalid quaternion(s)")
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assert( ! approx(norm(a+b),0), "Quaternions cannot be opposed" )
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a+b;
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assert( Q_is_quat(a) && Q_is_quat(a), "Invalid quaternion(s)")
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assert( ! approx(norm(a+b),0), "Quaternions cannot be opposed" )
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a+b;
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// Function: Q_Sub()
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@ -189,9 +189,9 @@ function Q_Add(a, b) =
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// Subtracts each part of quaternion `b` from quaternion `a`.
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// The returned quaternion is usually not normalized.
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function Q_Sub(a, b) =
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assert( Q_is_quat(a) && Q_is_quat(a), "Invalid quaternion(s)")
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assert( ! approx(a,b), "Quaternions cannot be equal" )
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a-b;
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assert( Q_is_quat(a) && Q_is_quat(a), "Invalid quaternion(s)")
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assert( ! approx(a,b), "Quaternions cannot be equal" )
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a-b;
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// Function: Q_Mul()
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@ -201,13 +201,13 @@ function Q_Sub(a, b) =
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// Multiplies quaternion `a` by quaternion `b`.
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// The returned quaternion is normalized if both `a` and `b` are normalized
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function Q_Mul(a, b) =
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assert( Q_is_quat(a) && Q_is_quat(b), "Invalid quaternion(s)")
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[
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a[3]*b.x + a.x*b[3] + a.y*b.z - a.z*b.y,
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a[3]*b.y - a.x*b.z + a.y*b[3] + a.z*b.x,
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a[3]*b.z + a.x*b.y - a.y*b.x + a.z*b[3],
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a[3]*b[3] - a.x*b.x - a.y*b.y - a.z*b.z,
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];
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assert( Q_is_quat(a) && Q_is_quat(b), "Invalid quaternion(s)")
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[
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a[3]*b.x + a.x*b[3] + a.y*b.z - a.z*b.y,
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a[3]*b.y - a.x*b.z + a.y*b[3] + a.z*b.x,
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a[3]*b.z + a.x*b.y - a.y*b.x + a.z*b[3],
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a[3]*b[3] - a.x*b.x - a.y*b.y - a.z*b.z,
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];
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// Function: Q_Cumulative()
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@ -235,16 +235,16 @@ function Q_Cumulative(v, _i=0, _acc=[]) =
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// Q_Dot(a, b)
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// Description: Calculates the dot product between quaternions `a` and `b`.
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function Q_Dot(a, b) =
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assert( Q_is_quat(a) && Q_is_quat(b), "Invalid quaternion(s)" )
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a*b;
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assert( Q_is_quat(a) && Q_is_quat(b), "Invalid quaternion(s)" )
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a*b;
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// Function: Q_Neg()
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// Usage:
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// Q_Neg(q)
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// Description: Returns the negative of quaternion `q`.
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function Q_Neg(q) =
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assert( Q_is_quat(q), "Invalid quaternion" )
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-q;
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assert( Q_is_quat(q), "Invalid quaternion" )
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-q;
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// Function: Q_Conj()
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@ -252,8 +252,8 @@ function Q_Neg(q) =
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// Q_Conj(q)
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// Description: Returns the conjugate of quaternion `q`.
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function Q_Conj(q) =
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assert( Q_is_quat(q), "Invalid quaternion" )
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[-q.x, -q.y, -q.z, q[3]];
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assert( Q_is_quat(q), "Invalid quaternion" )
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[-q.x, -q.y, -q.z, q[3]];
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// Function: Q_Inverse()
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@ -261,9 +261,9 @@ function Q_Conj(q) =
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// qc = Q_Inverse(q)
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// Description: Returns the multiplication inverse of quaternion `q` that is normalized only if `q` is normalized.
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function Q_Inverse(q) =
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assert( Q_is_quat(q), "Invalid quaternion" )
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let(q = _Qnorm(q) )
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[-q.x, -q.y, -q.z, q[3]];
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assert( Q_is_quat(q), "Invalid quaternion" )
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let(q = _Qnorm(q) )
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[-q.x, -q.y, -q.z, q[3]];
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// Function: Q_Norm()
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@ -273,8 +273,8 @@ function Q_Inverse(q) =
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// Returns the `norm()` "length" of quaternion `q`.
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// Normalized quaternions have unitary norm.
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function Q_Norm(q) =
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assert( Q_is_quat(q), "Invalid quaternion" )
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norm(q);
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assert( Q_is_quat(q), "Invalid quaternion" )
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norm(q);
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// Function: Q_Normalize()
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@ -282,8 +282,8 @@ function Q_Norm(q) =
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// Q_Normalize(q)
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// Description: Normalizes quaternion `q`, so that norm([W,X,Y,Z]) == 1.
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function Q_Normalize(q) =
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assert( Q_is_quat(q) , "Invalid quaternion" )
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q/norm(q);
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assert( Q_is_quat(q) , "Invalid quaternion" )
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q/norm(q);
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// Function: Q_Dist()
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@ -291,8 +291,8 @@ function Q_Normalize(q) =
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// Q_Dist(q1, q2)
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// Description: Returns the "distance" between two quaternions.
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function Q_Dist(q1, q2) =
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assert( Q_is_quat(q1) && Q_is_quat(q2), "Invalid quaternion(s)" )
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norm(q2-q1);
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assert( Q_is_quat(q1) && Q_is_quat(q2), "Invalid quaternion(s)" )
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norm(q2-q1);
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// Function: Q_Slerp()
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@ -318,25 +318,23 @@ function Q_Dist(q1, q2) =
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// Qrot(q) right(80) cube([10,10,1]);
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// #sphere(r=80);
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function Q_Slerp(q1, q2, u, _dot) =
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is_undef(_dot)
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? assert(is_num(u) || is_range(u) || is_num(0*u*u), "Invalid interpolation coefficient(s)")
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assert(Q_is_quat(q1) && Q_is_quat(q2), "Invalid quaternion(s)" )
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let(
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_dot = q1*q2,
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q1 = q1/norm(q1),
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q2 = _dot<0 ? -q2/norm(q2) : q2/norm(q2),
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dot = abs(_dot)
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)
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! is_num(u)
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? [for (uu=u) Q_Slerp(q1, q2, uu, dot)]
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: Q_Slerp(q1, q2, u, dot)
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: _dot>0.9995
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? _Qnorm(q1 + u*(q2-q1))
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: let(
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theta = u*acos(_dot),
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q3 = _Qnorm(q2 - _dot*q1)
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)
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_Qnorm(q1*cos(theta) + q3*sin(theta));
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is_undef(_dot)
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? assert(is_finite(u) || is_range(u) || is_vector(u), "Invalid interpolation coefficient(s)")
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assert(Q_is_quat(q1) && Q_is_quat(q2), "Invalid quaternion(s)" )
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let(
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_dot = q1*q2,
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q1 = q1/norm(q1),
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q2 = _dot<0 ? -q2/norm(q2) : q2/norm(q2),
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dot = abs(_dot)
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)
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! is_finite(u) ? [for (uu=u) Q_Slerp(q1, q2, uu, dot)] :
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Q_Slerp(q1, q2, u, dot)
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: _dot>0.9995
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? _Qnorm(q1 + u*(q2-q1))
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: let( theta = u*acos(_dot),
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q3 = _Qnorm(q2 - _dot*q1)
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)
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_Qnorm(q1*cos(theta) + q3*sin(theta));
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// Function: Q_Matrix3()
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@ -345,12 +343,12 @@ function Q_Slerp(q1, q2, u, _dot) =
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// Description:
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// Returns the 3x3 rotation matrix for the given normalized quaternion q.
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function Q_Matrix3(q) =
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let( q = Q_Normalize(q) )
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[
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[1-2*q[1]*q[1]-2*q[2]*q[2], 2*q[0]*q[1]-2*q[2]*q[3], 2*q[0]*q[2]+2*q[1]*q[3]],
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[ 2*q[0]*q[1]+2*q[2]*q[3], 1-2*q[0]*q[0]-2*q[2]*q[2], 2*q[1]*q[2]-2*q[0]*q[3]],
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[ 2*q[0]*q[2]-2*q[1]*q[3], 2*q[1]*q[2]+2*q[0]*q[3], 1-2*q[0]*q[0]-2*q[1]*q[1]]
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];
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let( q = Q_Normalize(q) )
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[
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[1-2*q[1]*q[1]-2*q[2]*q[2], 2*q[0]*q[1]-2*q[2]*q[3], 2*q[0]*q[2]+2*q[1]*q[3]],
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[ 2*q[0]*q[1]+2*q[2]*q[3], 1-2*q[0]*q[0]-2*q[2]*q[2], 2*q[1]*q[2]-2*q[0]*q[3]],
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[ 2*q[0]*q[2]-2*q[1]*q[3], 2*q[1]*q[2]+2*q[0]*q[3], 1-2*q[0]*q[0]-2*q[1]*q[1]]
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];
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// Function: Q_Matrix4()
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@ -359,13 +357,13 @@ function Q_Matrix3(q) =
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// Description:
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// Returns the 4x4 rotation matrix for the given normalized quaternion q.
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function Q_Matrix4(q) =
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let( q = Q_Normalize(q) )
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[
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[1-2*q[1]*q[1]-2*q[2]*q[2], 2*q[0]*q[1]-2*q[2]*q[3], 2*q[0]*q[2]+2*q[1]*q[3], 0],
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[ 2*q[0]*q[1]+2*q[2]*q[3], 1-2*q[0]*q[0]-2*q[2]*q[2], 2*q[1]*q[2]-2*q[0]*q[3], 0],
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[ 2*q[0]*q[2]-2*q[1]*q[3], 2*q[1]*q[2]+2*q[0]*q[3], 1-2*q[0]*q[0]-2*q[1]*q[1], 0],
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[ 0, 0, 0, 1]
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];
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let( q = Q_Normalize(q) )
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[
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[1-2*q[1]*q[1]-2*q[2]*q[2], 2*q[0]*q[1]-2*q[2]*q[3], 2*q[0]*q[2]+2*q[1]*q[3], 0],
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[ 2*q[0]*q[1]+2*q[2]*q[3], 1-2*q[0]*q[0]-2*q[2]*q[2], 2*q[1]*q[2]-2*q[0]*q[3], 0],
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[ 2*q[0]*q[2]-2*q[1]*q[3], 2*q[1]*q[2]+2*q[0]*q[3], 1-2*q[0]*q[0]-2*q[1]*q[1], 0],
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[ 0, 0, 0, 1]
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];
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// Function: Q_Axis()
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@ -375,9 +373,9 @@ function Q_Matrix4(q) =
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// Returns the axis of rotation of a normalized quaternion `q`.
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// The input doesn't need to be normalized.
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function Q_Axis(q) =
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assert( Q_is_quat(q) , "Invalid quaternion" )
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let( d = norm(_Qvec(q)) )
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approx(d,0)? [0,0,1] : _Qvec(q)/d;
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assert( Q_is_quat(q) , "Invalid quaternion" )
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let( d = norm(_Qvec(q)) )
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approx(d,0)? [0,0,1] : _Qvec(q)/d;
|
||||
|
||||
// Function: Q_Angle()
|
||||
// Usage:
|
||||
|
|
@ -388,12 +386,13 @@ function Q_Axis(q) =
|
|||
// If both q1 and q2 are given, returns the angle (in degrees) between them.
|
||||
// The input quaternions don't need to be normalized.
|
||||
function Q_Angle(q1,q2) =
|
||||
assert(Q_is_quat(q1) && (is_undef(q2) || Q_is_quat(q2)), "Invalid quaternion(s)" )
|
||||
let( n1 = is_undef(q2)? norm(_Qvec(q1)): norm(q1) )
|
||||
is_undef(q2)
|
||||
? 2 * atan2(n1,_Qreal(q1))
|
||||
: 2 * acos(q1*q2/n1/norm(q2)) ;
|
||||
|
||||
assert(Q_is_quat(q1) && (is_undef(q2) || Q_is_quat(q2)), "Invalid quaternion(s)" )
|
||||
let( n1 = is_undef(q2)? norm(_Qvec(q1)): norm(q1) )
|
||||
is_undef(q2)
|
||||
? 2 * atan2(n1,_Qreal(q1))
|
||||
: let( q1 = q1/norm(q1),
|
||||
q2 = q2/norm(q2) )
|
||||
4 * atan2(norm(q1 - q2), norm(q1 + q2));
|
||||
|
||||
// Function&Module: Qrot()
|
||||
// Usage: As Module
|
||||
|
|
@ -425,9 +424,9 @@ module Qrot(q) {
|
|||
}
|
||||
|
||||
function Qrot(q,p) =
|
||||
is_undef(p)? Q_Matrix4(q) :
|
||||
is_vector(p)? Qrot(q,[p])[0] :
|
||||
apply(Q_Matrix4(q), p);
|
||||
is_undef(p)? Q_Matrix4(q) :
|
||||
is_vector(p)? Qrot(q,[p])[0] :
|
||||
apply(Q_Matrix4(q), p);
|
||||
|
||||
|
||||
// Module: Qrot_copies()
|
||||
|
|
@ -457,24 +456,24 @@ module Qrot_copies(quats) for (q=quats) Qrot(q) children();
|
|||
// It doesn't check whether R is in fact a rotation matrix.
|
||||
// If R is not a rotation, the returned quaternion is an unpredictable quaternion .
|
||||
function Q_Rotation(R) =
|
||||
assert( is_matrix(R,3,3) || is_matrix(R,4,4) ,
|
||||
"Matrix is neither 3x3 nor 4x4")
|
||||
let( tr = R[0][0]+R[1][1]+R[2][2] ) // R trace
|
||||
tr>0
|
||||
? let( r = 1+tr )
|
||||
_Qnorm( _Qset([ R[1][2]-R[2][1], R[2][0]-R[0][2], R[0][1]-R[1][0] ], -r ) )
|
||||
: let( i = max_index([ R[0][0], R[1][1], R[2][2] ]),
|
||||
r = 1 + 2*R[i][i] -R[0][0] -R[1][1] -R[2][2] )
|
||||
i==0 ? _Qnorm( _Qset( [ 4*r, (R[1][0]+R[0][1]), (R[0][2]+R[2][0]) ], (R[2][1]-R[1][2])) ):
|
||||
i==1 ? _Qnorm( _Qset( [ (R[1][0]+R[0][1]), 4*r, (R[2][1]+R[1][2]) ], (R[0][2]-R[2][0])) )
|
||||
: _Qnorm( _Qset( [ (R[2][0]+R[0][2]), (R[1][2]+R[2][1]), 4*r ], (R[1][0]-R[0][1])) );
|
||||
assert( is_matrix(R,3,3) || is_matrix(R,4,4) ,
|
||||
"Matrix is neither 3x3 nor 4x4")
|
||||
let( tr = R[0][0]+R[1][1]+R[2][2] ) // R trace
|
||||
tr>0
|
||||
? let( r = 1+tr )
|
||||
_Qnorm( _Qset([ R[1][2]-R[2][1], R[2][0]-R[0][2], R[0][1]-R[1][0] ], -r ) )
|
||||
: let( i = max_index([ R[0][0], R[1][1], R[2][2] ]),
|
||||
r = 1 + 2*R[i][i] -R[0][0] -R[1][1] -R[2][2] )
|
||||
i==0 ? _Qnorm( _Qset( [ 4*r, (R[1][0]+R[0][1]), (R[0][2]+R[2][0]) ], (R[2][1]-R[1][2])) ):
|
||||
i==1 ? _Qnorm( _Qset( [ (R[1][0]+R[0][1]), 4*r, (R[2][1]+R[1][2]) ], (R[0][2]-R[2][0])) ):
|
||||
_Qnorm( _Qset( [ (R[2][0]+R[0][2]), (R[1][2]+R[2][1]), 4*r ], (R[1][0]-R[0][1])) ) ;
|
||||
|
||||
|
||||
// Function&Module: Q_Rotation_path(q1, n, [q2])
|
||||
// Usage as a function:
|
||||
// Usage: As a function
|
||||
// path = Q_Rotation_path(q1, n, q2);
|
||||
// path = Q_Rotation_path(q1, n);
|
||||
// Usage as a module:
|
||||
// Usage: As a module
|
||||
// Q_Rotation_path(q1, n, q2) ...
|
||||
// Description:
|
||||
// If q2 is undef and it is called as a function, the path, with length n+1 (n>=1), will be the
|
||||
|
|
@ -515,20 +514,20 @@ function Q_Rotation(R) =
|
|||
// right(80) cube([10,10,1]);
|
||||
// #sphere(r=80);
|
||||
function Q_Rotation_path(q1, n=1, q2) =
|
||||
assert( Q_is_quat(q1) && (is_undef(q2) || Q_is_quat(q2) ), "Invalid quaternion(s)" )
|
||||
assert( is_num(0*n) && n>=1 && n==floor(n), "Invalid integer" )
|
||||
assert( is_undef(q2) || ! approx(norm(q1+q2),0), "Quaternions cannot be opposed" )
|
||||
is_undef(q2)
|
||||
? [for( i=0, dR=Q_Matrix4(q1), R=dR; i<=n; i=i+1, R=dR*R ) R]
|
||||
: let( q2 = Q_Normalize( q1*q2<0 ? -q2: q2 ) )
|
||||
let( dq = Q_pow( Q_Mul( q2, Q_Inverse(q1) ), 1/n ),
|
||||
dR = Q_Matrix4(dq) )
|
||||
[for( i=0, R=Q_Matrix4(q1); i<=n; i=i+1, R=dR*R ) R];
|
||||
assert( Q_is_quat(q1) && (is_undef(q2) || Q_is_quat(q2) ), "Invalid quaternion(s)" )
|
||||
assert( is_finite(n) && n>=1 && n==floor(n), "Invalid integer" )
|
||||
assert( is_undef(q2) || ! approx(norm(q1+q2),0), "Quaternions cannot be opposed" )
|
||||
is_undef(q2)
|
||||
? [for( i=0, dR=Q_Matrix4(q1), R=dR; i<=n; i=i+1, R=dR*R ) R]
|
||||
: let( q2 = Q_Normalize( q1*q2<0 ? -q2: q2 ),
|
||||
dq = Q_pow( Q_Mul( q2, Q_Inverse(q1) ), 1/n ),
|
||||
dR = Q_Matrix4(dq) )
|
||||
[for( i=0, R=Q_Matrix4(q1); i<=n; i=i+1, R=dR*R ) R];
|
||||
|
||||
module Q_Rotation_path(q1, n=1, q2) {
|
||||
for(Mi=Q_Rotation_path(q1, n, q2))
|
||||
multmatrix(Mi)
|
||||
children();
|
||||
for(Mi=Q_Rotation_path(q1, n, q2))
|
||||
multmatrix(Mi)
|
||||
children();
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -559,15 +558,15 @@ module Q_Rotation_path(q1, n=1, q2) {
|
|||
// Qrot(q) right(80) cube([10,10,1]);
|
||||
// #sphere(r=80);
|
||||
function Q_Nlerp(q1,q2,u) =
|
||||
assert(Q_is_quat(q1) && Q_is_quat(q2), "Invalid quaternion(s)" )
|
||||
assert( ! approx(norm(q1+q2),0), "Quaternions cannot be opposed" )
|
||||
assert(is_num(0*u) || is_range(u) || (is_list(u) && is_num(0*u*u)) ,
|
||||
"Invalid interpolation coefficient(s)" )
|
||||
let( q1 = Q_Normalize(q1),
|
||||
q2 = Q_Normalize(q2) )
|
||||
!is_num(u)
|
||||
? [for (ui=u) _Qnorm((1-ui)*q1 + ui*q2 ) ]
|
||||
: _Qnorm((1-u)*q1 + u*q2 );
|
||||
assert(is_finite(u) || is_range(u) || is_vector(u) ,
|
||||
"Invalid interpolation coefficient(s)" )
|
||||
assert(Q_is_quat(q1) && Q_is_quat(q2), "Invalid quaternion(s)" )
|
||||
assert( ! approx(norm(q1+q2),0), "Quaternions cannot be opposed" )
|
||||
let( q1 = Q_Normalize(q1),
|
||||
q2 = Q_Normalize(q2) )
|
||||
is_num(u)
|
||||
? _Qnorm((1-u)*q1 + u*q2 )
|
||||
: [for (ui=u) _Qnorm((1-ui)*q1 + ui*q2 ) ];
|
||||
|
||||
|
||||
// Function: Q_Squad()
|
||||
|
|
@ -610,11 +609,11 @@ function Q_Nlerp(q1,q2,u) =
|
|||
// Qrot(q) right(80) cube([10,10,1]);
|
||||
// #sphere(r=80);
|
||||
function Q_Squad(q1,q2,q3,q4,u) =
|
||||
assert(is_num(0*u) || is_range(u) || (is_list(u) && is_num(0*u*u)) ,
|
||||
"Invalid interpolation coefficient(s)" )
|
||||
is_num(u)
|
||||
? Q_Slerp( Q_Slerp(q1,q4,u), Q_Slerp(q2,q3,u), 2*u*(1-u))
|
||||
: [for(ui=u) Q_Slerp( Q_Slerp(q1,q4,ui), Q_Slerp(q2,q3,ui), 2*ui*(1-ui) ) ];
|
||||
assert(is_finite(u) || is_range(u) || is_vector(u) ,
|
||||
"Invalid interpolation coefficient(s)" )
|
||||
is_num(u)
|
||||
? Q_Slerp( Q_Slerp(q1,q4,u), Q_Slerp(q2,q3,u), 2*u*(1-u))
|
||||
: [for(ui=u) Q_Slerp( Q_Slerp(q1,q4,ui), Q_Slerp(q2,q3,ui), 2*ui*(1-ui) ) ];
|
||||
|
||||
|
||||
// Function: Q_exp()
|
||||
|
|
@ -624,9 +623,9 @@ function Q_Squad(q1,q2,q3,q4,u) =
|
|||
// Returns the quaternion that is the exponential of the quaternion q in base e
|
||||
// The returned quaternion is usually not normalized.
|
||||
function Q_exp(q) =
|
||||
assert( is_vector(q,4), "Input is not a valid quaternion")
|
||||
let( nv = norm(_Qvec(q)) ) // q may be equal to zero!
|
||||
exp(_Qreal(q))*Quat(_Qvec(q),2*nv);
|
||||
assert( is_vector(q,4), "Input is not a valid quaternion")
|
||||
let( nv = norm(_Qvec(q)) ) // q may be equal to zero here!
|
||||
exp(_Qreal(q))*Quat(_Qvec(q),2*nv);
|
||||
|
||||
|
||||
// Function: Q_ln()
|
||||
|
|
@ -636,12 +635,11 @@ function Q_exp(q) =
|
|||
// Returns the quaternion that is the natural logarithm of the quaternion q.
|
||||
// The returned quaternion is usually not normalized and may be zero.
|
||||
function Q_ln(q) =
|
||||
assert(Q_is_quat(q), "Input is not a valid quaternion")
|
||||
let( nq = norm(q),
|
||||
nv = norm(_Qvec(q)) )
|
||||
approx(nv,0)
|
||||
? _Qset([0,0,0] , ln(nq) )
|
||||
: _Qset(_Qvec(q)*atan2(nv,_Qreal(q))/nv, ln(nq));
|
||||
assert(Q_is_quat(q), "Input is not a valid quaternion")
|
||||
let( nq = norm(q),
|
||||
nv = norm(_Qvec(q)) )
|
||||
approx(nv,0) ? _Qset([0,0,0] , ln(nq) ) :
|
||||
_Qset(_Qvec(q)*atan2(nv,_Qreal(q))/nv, ln(nq));
|
||||
|
||||
|
||||
// Function: Q_pow()
|
||||
|
|
@ -651,11 +649,10 @@ function Q_ln(q) =
|
|||
// Returns the quaternion that is the power of the quaternion q to the real exponent r.
|
||||
// The returned quaternion is normalized if `q` is normalized.
|
||||
function Q_pow(q,r=1) =
|
||||
// Q_exp(r*Q_ln(q));
|
||||
assert( Q_is_quat(q) && is_num(0*r),
|
||||
"Invalid inputs")
|
||||
let( theta = 2*atan2(norm(_Qvec(q)),_Qreal(q)) )
|
||||
Quat(_Qvec(q), r*theta);
|
||||
assert( Q_is_quat(q) && is_finite(r),
|
||||
"Invalid inputs")
|
||||
let( theta = 2*atan2(norm(_Qvec(q)),_Qreal(q)) )
|
||||
Quat(_Qvec(q), r*theta); // Q_exp(r*Q_ln(q));
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Reference in a new issue