• "Z_etan&theta" should be "Z_etan&theta"
• change
  ... and &phi is the half-angle of view."
  to
  "... and &phi is the half-angle of view - the angle made by the view direction and each of the planar surfaces of the view frustum (assumes the frustum has an aspect ratio of 1, i.e., a square cross section).

QuatRot(&theta,(x,y,z)) &equiv [cos(&theta/2), sin(&theta/2)(x,y,z)]

q &equiv Quatrot(QuatRot(&theta,(x,y,z))
  = [cos(&theta/2), sin(&theta/2)(x,y,z)]
  = [cos(-&theta/2), -sin(&theta/2)(-x,-y,-z)]
  = [cos(-&theta/2), sin(-&theta/2)(-x,-y,-z)]
  &equiv Quatrot(-&theta,-(x,y,z)) &equiv -q

• The 'p' in the equation that should be a 'q'
• The first rotation, which looks like:

  Rotq-1
  

  should be:

  Rotq-1
  

  = 0.944 + ((0.73-0.70)/(0.75-0.70))(0.959 - 0.944)

double evaluate_polynomial(polynomial_td *poly, double u)
{
    int            i;
    double     value;

    value = poly->coeff[poly->degree];
    for (i=poly->degree-1; i >= 0; i--) {
        value = poly->coeff[i] + u*value;
    }
    return value;
}

sin((1-u)*θ)

Slerp(q0,q1,u) = q0(q0-1q1)u
where qu =  [cos(uθ), v*sin(uθ)]
and v is a 3D unit vector

   
         double(p,q) = 2*(p⋅q)q - p

temp = slerp(qn,an,1/2) = qn + an

temp = slerp(qn,an,1/2) = (qn + an) / ||qn + an||

• The equations are for a bend in the y-z plane while the plot shows a bend in the x-z plane
• On the right, the conditional equations for &theta should have a new first line of '= 0 z The third equation should be for z: "z' = ..."

(1-t)m-jtj

(1-t)m-jtj

C[i][j] = αC1[i][j] + (1+&alpha)C2[i][j]

• Toward the bottom of the code in three places, replace "->arc" with "->arcPtr"
• At the bottom of the code, replace "pop(matrix)" with "matrix = pop()"; also, in the middle of the code, "matrix = Pop()" should be "matrix = pop()"

• In the first equation,

  acos(...) = ....
  

  should be:

  cos(...) = ...
  

  However, it would more direct to use tangent:

  tan(&thetaT) = Y/X
  

  and therefore use arctangent in the second line. However, because of the ambiguity that results due to Y/X = -Y/-X, it is better to use a two-argument arctangent function if one is available:

  &thetaT = atan2(Y,X)
  

• In the last equation in the figure, the numerator on the right contains:

  -X2+Y2
  

  and it should be:

  -(X2+Y2)
  

Y = [px,py,pz,αx,αy,αz]T

J+ = (JTJ)-1JT = JT(JJT)-1

 230, 220, 210

 -30, -20, -10

  root
      joint Chest offset 0 5.21 0
                   3 DOFs: Zrotation Yrotation, Xrotation
                    Limits: (-180,180)  (-90,90) (0,270)
           joint Neck
                offset 0 5.45 0
                3 DOFs: Zrotation Yrotation, Xrotation
     ...
      joint Left UpperLeg
                offset 3.91 0.0 0.0
                3 DOFs: Xrotation Yrotation, Zrotation
          joint LeftLowerLeg
               offset 3.91 0.0 0.0
               1 DOF: Xrotation
         ...

θ(t) = f(&theta,t)

θ′(t) = f(&theta,t)

• Change:
  "The damping force of a spring ..."
  to:
  "The damping force ..."
  
• Change"
  "... velocity of the spring length ..."
  to:
  "... velocity of the distance between the objects ..."
• Change:
  "... to a change in spring length ..."
  to:
  "... to a change in the distance between the objects ..."

&tau = I&alpha

typedef particle_struct struct {

typedef struct particle_struct {

typedef particleSystem_struct struct {

typedef struct particleSystem_struct {

addVector(array2,array2,array2,n)

addVector(array1,array1,array2,n)

• In the left column vector, the second element should be negated.
• In the first row of the 3 X 3 matrix, the second element should be -A_z
• The third equal sign should be removed

E(p) = ax + by + cz + d

E(p) = apx + bpy + cpz + d

v(tt+1) = v(tt) - (v(tt)⋅N)N + k*(v(tt)⋅N)N
        = v(tt) + (k-1)*(v(tt)⋅N)N

• The inequality should be:

  0≤ε≤1
  

• Note that 'k' was used as the coefficient of restitution in the case of directly modifying the normal component of velocity whereas &epsilon is used here in the discussion of computing the impulse force of collision.
• It is also worth noting that if the coefficient is less than unity, the collision is inelastic and kinetic energy is not conserved.

vrel = (pA(t) - pB(t))n

• In the first line, the second '=' should be a '+'
  
• In the second line, the 'w' should be &omega

• the last plus sign '+', should be a '-'
• the n should be a dot product with then entire rest of the denominator

• The second line should be:

  Compute Vrelative = dot(N,(VA-VB))   ; Eq. 7.63
  

• The 3 equations cited in the comments (which includes the line above) should be:

  Eq. 7.60, Eq. 7.63, and Eq. 7.65
  

• The first 'else' statement should be:

  else if Vrelative &ge -threshold
  

f(x,t)

f(s,t)

&thetai(x,y,t0)

&thetai(x,z,t0)

&thetai(x,z,t0) = xi/Li

• The reference to Equation 8.10 should be to Equation 8.23
• The reference to Equation 8.13 should be to Equation 8.26

01047196

.01047196

δF/δx + δF/δy + δF/δz

∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

∇•F = δF/δx + δF/δy + δF/δz

∇•F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

• In the equation for 't', 'K' should be 'k'
• In the 5th line of the equation, there is a left parenthesis that should not be there.

• The sign of the s⁴ term should be positive
• There parenthesis around the s⁶ term is not necessary

• "If f is the corner surface, then the coverage is &beta = (s+t)/2"
  Because coverage is a triangle, the area is:

   &beta = st/2
  

• "If b is the corner surface, then &beta = 1.0 - (s+t)/2"
  the coverage should be:

  &beta = 1 - st/2
  

• Change:
  Cij = ...
  to:
  C_ij = ...
• The sum over the term:

  AjkBkj
  

  should be:

  AikBkj
  

L31⋅y1

L31y1

typedef  struct  xyz_struct {
float    x,y,z;
xyz_td;
}

typedef  struct  xyz_struct {
float    x,y,z;
} xyz_td;

xyz_tdp;

xyz_td  p;

xyz_tdp;

xyz_td  p;

Rot[0,x,y,z]

Rot[θ,x,y,z]

2xy-2sy

2xz-2sy

• The second term of the third row of the 3x3 matrix should be -I_yz instead of I_yz.
• In the first integral (Ixx), each of y and z should be squared

-Iyz - MYZ

r - r0 = svvi

ri - r0 = svvi

• The numerator of left side of the equation is:

  ui
  

  It should be:

  vi
  

• The denominator of the third expression in the equation is:

  fv
  

  It should be:

  fv
  

(ri = r0)

(ri - r0)

• The last element of the left column vectors is:

  W11
  

  It should be:

  W11
  

• In the rightmost expression, the column vector is multiplied by:

  1/||W'6||
  

  It should be:

  1/||W11||
  

  Also, the dot indicating multiplication is not needed.