In-Plane Movement Overhead View

\documentclass[12pt]{article}

\usepackage[paperwidth=215pt, paperheight=215pt,margin=12pt]{geometry}
\usepackage{color,tikz,ifthen,animate,pgf}

\begin{document}

% This code will simulate a pitch based on the 9-parameter PITCHf/x model, including the pitch plane and projections for PITCHf/x movement without (red) and with (blue dashed) accounted for.

% Written by Matthew Mata, January 2017.

\thispagestyle{empty}

% Set the counter
\newcounter{m}
\setcounter{m}{0}

% Set the PITCHf/x parameters
\pgfmathsetmacro{\xo}{1.958}
\pgfmathsetmacro{\yo}{50.0}
\pgfmathsetmacro{\zo}{6.041}
\pgfmathsetmacro{\vxo}{-0.469}
\pgfmathsetmacro{\vyo}{-115.739}
\pgfmathsetmacro{\vzo}{-0.622}
\pgfmathsetmacro{\ax}{-10.947}
\pgfmathsetmacro{\ay}{23.455}
\pgfmathsetmacro{\az}{-32.665}

% Set gravity
\pgfmathsetmacro{\g}{-32.174}

% Set the binormal vector
\pgfmathsetmacro{\Bx}{\vyo*\az - \vzo*\ay}
\pgfmathsetmacro{\By}{\vzo*\ax - \vxo*\az}
\pgfmathsetmacro{\Bz}{\vxo*\ay - \vyo*\ax}
\pgfmathsetmacro{\Bnorm}{100*sqrt((0.01*\Bx)*(0.01*\Bx) + (0.01*\By)*(0.01*\By) + (0.01*\Bz)*(0.01*\Bz))}
\pgfmathsetmacro{\Bx}{\Bx/\Bnorm}
\pgfmathsetmacro{\By}{\By/\Bnorm}
\pgfmathsetmacro{\Bz}{\Bz/\Bnorm}

% Find the fixed B-coordinate
\pgfmathsetmacro{\Bfixed}{\Bx*\xo + \By*\yo + \Bz*\zo}

% Set the vector in the direction of home plate, u
\pgfmathsetmacro{\Ux}{(\Bx/abs(\Bx))*(-\By)/sqrt(\Bx*\Bx + \By*\By)}
\pgfmathsetmacro{\Uy}{abs(\Bx)/sqrt(\Bx*\Bx + \By*\By)}
\pgfmathsetmacro{\Uz}{0}

% Set the vector in the direction of movement, w
\pgfmathsetmacro{\signW}{(\Bx*\Uy-\By*\Ux)/abs(\Bx*\Uy-\By*\Ux)}
\pgfmathsetmacro{\Wx}{\signW*(-\Bz*\Uy)}
\pgfmathsetmacro{\Wy}{\signW*(\Bz*\Ux)}
\pgfmathsetmacro{\Wz}{\signW*(\Bx*\Uy-\By*\Ux)}
\pgfmathsetmacro{\Wnorm}{sqrt(\Wx*\Wx + \Wy*\Wy + \Wz*\Wz)}
\pgfmathsetmacro{\Wx}{\Wx/\Wnorm}
\pgfmathsetmacro{\Wy}{\Wy/\Wnorm}
\pgfmathsetmacro{\Wz}{\Wz/\Wnorm}

% Find the position, velocity, and acceleration in uw-space
\pgfmathsetmacro{\uo}{\Ux*\xo + \Uy*\yo + \Uz*\zo}
\pgfmathsetmacro{\vuo}{\Ux*\vxo + \Uy*\vyo + \Uz*\vzo}
\pgfmathsetmacro{\au}{\Ux*\ax + \Uy*\ay + \Uz*\az}
\pgfmathsetmacro{\wo}{\Wx*\xo + \Wy*\yo + \Wz*\zo}
\pgfmathsetmacro{\vwo}{\Wx*\vxo + \Wy*\vyo + \Wz*\vzo}
\pgfmathsetmacro{\aw}{\Wx*\ax + \Wy*\ay + \Wz*\az}
\pgfmathsetmacro{\gw}{\Wz*\g}

% Find the time to home plate from 50 feet
\pgfmathsetmacro{\r}{\vyo/\ay}
\pgfmathsetmacro{\s}{2*(\yo-(17/12))/\ay}
\pgfmathsetmacro{\tplate}{-\r - sqrt(\r*\r - \s)}

% Find the time of release at 55 feet
\pgfmathsetmacro{\u}{2*(\yo-55)/\ay}
\pgfmathsetmacro{\trel}{-\r - sqrt(\r*\r - \u)}

% Find the flight time of the pitch
\pgfmathsetmacro{\t}{\tplate - \trel}

% Set the end velocities
\pgfmathsetmacro{\vxend}{\vxo + \tplate*\ax}
\pgfmathsetmacro{\vyend}{\vyo + \tplate*\ay}
\pgfmathsetmacro{\vzend}{\vzo + \tplate*\az}

% Set the number of frames
\pgfmathtruncatemacro{\frames}{int(round(\t*60)+1)}

% Set the time increment
\pgfmathsetmacro{\dt}{\t/(\frames-1)}

\begin{center}
    \begin{animateinline}[poster=first,loop,controls]{60}
        \whiledo{\them < \frames}{
            \begin{tikzpicture}[scale=0.725]
                \clip(-4,-1) rectangle (4,7);
                % Plot the field
                \draw[green!75!black,fill=green!75!black] (-4,7) -- (4,7) -- (4,-1) -- (-4,-1) -- cycle;
                \draw[brown!75!black,fill=brown!75!black] (0,0) circle [radius=1.3];
                \draw[brown!75!black,fill=brown!75!black] (0,6.05) circle [radius=0.9];
                \draw[white!75!brown,fill=white!75!brown] (-0.1,6.05) -- (-0.1,6.1) -- (0.1,6.1) -- (0.1,6.05) -- cycle;
                \draw[thick, white!75!brown] (0.3708,0.3708) -- (6.364,6.364);
                \draw[thick, white!75!brown] (-0.3708,0.3708) -- (-6.364,6.364);
                \draw[white, thick, fill=white] (0,0) -- (0.0708,0.0708) -- (0.0708,0.1416) -- (-0.0708,0.1416) -- (-0.0708,0.0708) -- cycle;
                \draw[white!75!brown, thick] (0.1208,0.3708) -- (0.5208,0.3708) -- (0.5208,-0.2291) -- (0.1208,-0.2291) -- cycle;
                \draw[white!75!brown, thick] (-0.1208,0.3708) -- (-0.5208,0.3708) -- (-0.5208,-0.2291) -- (-0.1208,-0.2291) -- cycle;
                \draw[white!75!brown, thick] (0.179,-0.2291) -- (0.179,-0.8) -- (-0.179,-0.8) -- (-0.179,-0.2291);
                % Calculate the time increment
                \pgfmathsetmacro{\tinc}{\dt*\them + \trel};
                % Current flight time of the pitch
                \pgfmathsetmacro{\time}{\dt*\them};
                % Find the x and y positions of the pitch
                \pgfmathsetmacro{\xraw}{0.5*\ax*\tinc*\tinc + \vxo*\tinc + \xo};
                \pgfmathsetmacro{\yraw}{0.5*\ay*\tinc*\tinc + \vyo*\tinc + \yo};
                % Velocity of the pitch at the given time
                \pgfmathsetmacro{\vx}{\ax*\tinc + \vxo};
                \pgfmathsetmacro{\vy}{\ay*\tinc + \vyo};
                \pgfmathsetmacro{\vz}{\az*\tinc + \vzo};
                \pgfmathsetmacro{\vel}{sqrt((15*\vx/22)*(15*\vx/22) + (15*\vy/22)*(15*\vy/22) + (15*\vz/22)*(15*\vz/22))};
                % Time remaining
                \pgfmathsetmacro{\trem}{\tplate-\tinc};
                % Projection of the in-plane pitch excluding drag
                \pgfmathsetmacro{\uraw}{0.5*\au*\tinc*\tinc + \vuo*\tinc + \uo};
                \pgfmathsetmacro{\wraw}{0.5*\aw*\tinc*\tinc + \vwo*\tinc + \wo};
                \pgfmathsetmacro{\vu}{\au*\tinc + \vuo};
                \pgfmathsetmacro{\vw}{\aw*\tinc + \vwo};
                \pgfmathsetmacro{\uproj}{0.5*\au*(\tplate - \tinc)*(\tplate - \tinc) + \vu*(\tplate - \tinc) + \uraw};
                \pgfmathsetmacro{\wproj}{0.5*\gw*(\tplate - \tinc)*(\tplate - \tinc) + \vw*(\tplate - \tinc) + \wraw};
                \pgfmathsetmacro{\xplane}{\Ux*\uproj + \Wx*\wproj + \Bx*\Bfixed};
                % Calculate the drag
                \pgfmathsetmacro{\vxbar}{(\vx+\vxend)/2};
                \pgfmathsetmacro{\vybar}{(\vy+\vyend)/2};
                \pgfmathsetmacro{\vzbar}{(\vz+\vzend)/2};
                \pgfmathsetmacro{\vbar}{1.25*sqrt((\vxbar/1.25)*(\vxbar/1.25) + (\vybar/1.25)*(\vybar/1.25) + (\vzbar/1.25)*(\vzbar/1.25))};
                \pgfmathsetmacro{\vcoeff}{-abs(\ax*(\vxbar/\vbar) + \ay*(\vybar/\vbar) + (\az-\g)*(\vzbar/\vbar))};
                \pgfmathsetmacro{\axdrag}{\vcoeff*(\vxbar/\vbar)};
                \pgfmathsetmacro{\aydrag}{\vcoeff*(\vybar/\vbar)};
                \pgfmathsetmacro{\azdrag}{\g + \vcoeff*(\vzbar/\vbar)};
                % Contribution of drag in the w-direction
                \pgfmathsetmacro{\awdrag}{\Wx*\axdrag + \Wy*\aydrag + \Wz*\azdrag};
                % Projection of the in-plane pitch into the strike zone including drag
                \pgfmathsetmacro{\wprojdrag}{0.5*\awdrag*(\tplate - \tinc)*(\tplate - \tinc) + \vw*(\tplate - \tinc) + \wraw};
                \pgfmathsetmacro{\xplanedrag}{\Ux*\uproj + \Wx*\wprojdrag + \Bx*\Bfixed};
                % Plot a straight line from the ball to the projection without drag
                \draw[red] ({0.1*\xraw},{0.1*\yraw}) -- ({0.1*\xplane},{0.1*(17/12)});
                % Plot a curve from the ball to the projection with drag
                \pgfmathsetmacro{\framesadj}{\frames-1}
                \ifthenelse{ \them < \framesadj }{
                \draw[blue, domain=0:\trem, smooth, dashed] plot ({0.1*\Ux*(0.5*\au*\x*\x + \vu*\x + \uraw) + 0.1*\Wx*(0.5*\awdrag*\x*\x + \vw*\x + \wraw) +  0.1*\Bx*\Bfixed},{0.1*(0.5*\ay*\x*\x + \vy*\x + \yraw)});
                }
                {
                }
                % Plot the projection without drag
                \draw[red, ball color=red, shading=ball] ({0.1*\xplane},{0.1*(17/12)}) circle [radius=0.0125];
                % Plot the projection with drag
                \draw[blue, ball color=blue, shading=ball] ({0.1*\xplanedrag},{0.1*(17/12)}) circle [radius=0.0125];
                % Plot the ball
                \draw[white, ball color=white, shading=ball] ({0.1*\xraw},{0.1*\yraw}) circle [radius=0.0125];
                % Display the metrics
                \node[above right] at (-4,6) {Dist.: };
                \node[above left] at (-1.25,6) {\pgfmathprintnumber[precision=1,fixed]{\yraw}};
                \node[above right] at (-1.5,6) {ft};
                \node[above right] at (0,6) {Vel.: };
                \node[above left] at (2.75,6) {\pgfmathprintnumber[precision=1,fixed]{\vel}};
                \node[above left] at (4,5.9) {mph};
                \node[above right] at (-4,-1) {Time: };
                \node[above left] at (-1,-1) {\pgfmathprintnumber[precision=2,fixed]{\time}};
                \node[above right] at (-1.25,-1) {sec};
                \foreach \n in {0,...,\frames}{
                    \ifthenelse{\n < \them}{
                        \pgfmathsetmacro{\tshadow}{\dt*\n + \trel};
                        \pgfmathsetmacro{\xshadow}{0.5*\ax*\tshadow*\tshadow + \vxo*\tshadow + \xo};
                        \pgfmathsetmacro{\yshadow}{0.5*\ay*\tshadow*\tshadow + \vyo*\tshadow + \yo};
                        \draw[white, ball color=white, shading=ball, opacity=0.5] ({0.1*\xshadow},{0.1*\yshadow}) circle [radius=0.025];
                    }
                }
            \end{tikzpicture}
            \stepcounter{m}
            \ifthenelse{\them < \frames}{
                \newframe
            }
            {
                \end{animateinline} \relax
            }
        }
\end{center}

\end{document}