\documentclass{article}
\usepackage{epsfig}
\pagestyle{empty}
\begin{document}
$(t_x, t_y, t_z)$
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$\hat{x}$
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$(0,0,0)-(1,0,0)$
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$(0,0,0)-(0,1,0)$
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$(0,0,0)-(0,0,1)$
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$ (1,1,1) $
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$L_\infty$
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$L_1$
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$M_{i,j} = m_{i,j} * scalar$
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$i, j \in [0, 2]$
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$M_{i,j} = m0_{i,j} + m1_{i,j}$
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$M_{i,j} = m0_{i,j} - m1_{i,j}$
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$M_{ij} = \sum_{n=0}^2\left(m0_{nj} + m1_{in}\right)$
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$v_{i} = \sum_{n=0}^2 m_{i,n} * v_n$
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$i \in [0, 2]$
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$v_{i} = \sum_{n=0}^2 m_{n,i} * v_n$
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$m_{i,j} *= scalar$
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$m0_{i,j} += m1_{i,j}$
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$m0_{i,j} -= m1_{i,j}$
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$m0_{i,j} *= m1_{i,j}$
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$i, j \in [0, 3]$
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$v_{i} = \sum_{n=0}^3 m_{i,n} * v_n $
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$i \in [0, 3]$
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$v_{i} = \sum_{n=0}^3 m_{n,i} * v_n $
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$v_{i} = \sum_{n=0}^3\left(m_{i,n} * v_n + m_{i,3}\right)$
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$v_{i} = \sum_{n=0}^3\left(m_{n,i} * v_n + m_{3,i}\right)$
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$M_{ij} = \sum_{n=0}^3\left(m0_{nj} + m1_{in}\right)$
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$m_{i,j} = \sum_{k} m0_{i,k}*m1_{k,j}$
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$(3-2x)x^2$
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$(3-2t)t^2$
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$t = (x-min)/(max-min)$
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$ x^2 $
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$ x^3 $
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$ x^4 $
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$ x^n $
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$ b^e $
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$ e^x $
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$\nabla \cdot (\nabla \phi / |\nabla \phi|)$
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$|\nabla \phi|$
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$V_i = v_i * scalar$
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$i \in [0, 1]$
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$V_i = v0_i * v1_i$
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$V_i = scalar / v_i$
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$V_i = v_i / scalar$
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$V_i = v0_i / v1_i$
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$V_i = v0_i + v1_i$
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$V_i = v_i + scalar$
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$V_i = v0_i - v1_i$
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$V_i = v_i - scalar$
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$v_i *= scalar$
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$v0_i *= v1_i$
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$v_i /= scalar$
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$v0_i /= v1_i$
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$v_i += scalar$
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$v0_i += v1_i$
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$v0_i -= v1_i$
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$|\nabla\phi|\in[min,max]$
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$|\nabla\phi|^2\in[min^2,max^2]$
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$(i,j,k)$
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$2^{3 \times {\rm Log2Dim}}$
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$ (x=0, z=-1/g)$
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$ (x-xo)^2 + (z-zo)^2 = r^2 $
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$(x,y,z)$
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$8\times8\times8$
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$2^4\times2^4\times2^4 = 16\times16\times16$
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$2^5\times2^5\times2^5 = 32\times32\times32$
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$32\times16\times8 = 4096$
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$\Delta$
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$(x,y,z) = (\Delta i, \Delta j, \Delta k)$
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$3 \times 3$
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$(x,y,z) = (\Delta i + \Delta/2, \Delta j + \Delta/2, \Delta k + \Delta /2 )$
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$(0,0,0)$
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$(\Delta/2, \Delta/2, \Delta/2)$
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$x=0$
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$y=0$
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$z=0$
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$ijk = (0,0,0)$
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$(x,y,z) = (\Delta i , \Delta j ,\Delta k)$
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$(i-1/2,j,k)$
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$(i,j-1/2,k)$
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$(i,j,k-1/2)$
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$4 \times 4$
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$x_{range} = f(x_{domain})$
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$x_{domain} = f^{-1}(x_{range})$
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\end{document}
