CG标准函数库

港控/mmm° 2022-07-13 14:48 166阅读 0赞

原文地址：[http://blog.csdn.net/lcbcsdn/article/details/46848125][http_blog.csdn.net_lcbcsdn_article_details_46848125]

> ### （1）数学函数 ###

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 <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数</th> 
 <th align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 功能描述</th> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> abs(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回输入参数的绝对值</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> acos(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 反余切函数，输入参数范围为[-1,1]， 返回[0,π]区间的角度值</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> all(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果输入参数均不为0，则返回ture； 否则返回flase。&amp;&amp;运算</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> any(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 输入参数只要有其中一个不为0，则返回true。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> asin(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 反正弦函数,输入参数取值区间为<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> [−1,1]<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"> ，返回角度值范围为,&nbsp;<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> [−π2<span style="display:inline-block; position:static; border-width:0px 0px 0px 1.155em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px">,π2<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.521em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px">]<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.854em; overflow:hidden; width:0px; height:2.361em; color:rgb(255,255,255)"> </td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> atan(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 反正切函数，返回角度值范围为<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> [−π2<span style="display:inline-block; position:static; border-width:0px 0px 0px 1.155em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px">,π2<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.521em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px">]<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.854em; overflow:hidden; width:0px; height:2.361em; color:rgb(255,255,255)"> </td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> atan2(y,x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算y/x的反正切值。实际上和atan(x)函数功能完全一样，至少输入参数不同。atan(x) = atan2(x, float(1))。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> ceil(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 对输入参数向上取整。例如： ceil(float(1.3)) ，其返回值为2.0</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> clamp(x,a,b)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果x值小于a，则返回a； 如果x值大于b，返回b； 否则，返回x。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> cos(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回弧度x的余弦值。返回值范围为<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> [−1,1]<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"> </td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> cosh(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 双曲余弦（hyperbolic cosine）函数，计算x的双曲余弦值。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> cross(A,B)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回两个三元向量的叉积(cross product)。注意，输入参数必须是三元向量！</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> degrees(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 输入参数为弧度值(radians)，函数将其转换为角度值(degrees)</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> determinant(m)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算矩阵的行列式因子。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> dot(A,B)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回A和B的点积(dot product)。参数A和B可以是标量，也可以是向量（输入参数方面，点积和叉积函数有很大不同）。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> exp(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> ex<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"> 的值，e=2.71828182845904523536</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> exp2(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> 2x<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"> 的值</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> floor(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 对输入参数向下取整。例如floor(float(1.3))返回的值为1.0；但是floor(float(-1.3))返回的值为-2.0。该函数与ceil(x)函数相对应。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> fmod(x,y)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回x/y的余数。如果y为0，结果不可预料。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> frac(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回标量或矢量的小数</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> frexp(x, out i)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 将浮点数x分解为尾数和指数，即<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> x=m∗2i<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.218em; color:rgb(255,255,255)"> ， 返回m，并将指数存入i中；如果x为0，则尾数和指数都返回0</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> isfinite(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 判断标量或者向量中的每个数据是否是有限数，如果是返回true；否则返回false;</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> isinf(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 判断标量或者向量中的每个数据是否是无限，如果是返回true；否则返回false;</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> isnan(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 判断标量或者向量中的每个数据是否是非数据(not-a-number NaN)，如果是返回true；否则返回false;</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> ldexp(x, n)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> x∗2n<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"> 的值</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> lerp(a, b, f)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> (1−f)∗a+b∗f<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"> 或者<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> a+f∗(b−a)<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"> 的值。即在下限a和上限b之间进行插值，f表示权值。注意，如果a和b是向量，则权值f必须是标量或者等长的向量。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> lit(NdotL, NdotH, m)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> N表示法向量； L表示入射光向量； H表示半角向量； m表示高光系数。&nbsp; 函数计算环境光、散射光、镜面光的贡献，返回的4元向量。&nbsp; X位表示环境光的贡献，总是1.0;&nbsp; Y位代表散射光的贡献，如果&nbsp;<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> N∙L&lt;0<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.075em; color:rgb(255,255,255)"> ，则为0；否则为<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> N∙L<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"> &nbsp; Z位代表镜面光的贡献，如果<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> N∙L&lt;0<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.075em; color:rgb(255,255,255)"> &nbsp;或者<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> N∙H&lt;0<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.075em; color:rgb(255,255,255)"> ，则位0；否则为<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> (N∙L)m<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.354em; overflow:hidden; width:0px; height:1.432em; color:rgb(255,255,255)"> ; W位始终位1.0</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> log(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> ln(x)<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.289em; color:rgb(255,255,255)"> 的值，x必须大于0</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> log2(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> log(x)2<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.425em; overflow:hidden; width:0px; height:1.861em; color:rgb(255,255,255)"> 的值，x必须大于0</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> log10(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> log(x)10<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.496em; overflow:hidden; width:0px; height:1.861em; color:rgb(255,255,255)"> 的值，x必须大于0</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> max(a, b)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 比较两个标量或等长向量元素，返回最大值。</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> min(a,b)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 比较两个标量或等长向量元素，返回最小值。</td> 
 </tr> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> modf(x, out ip)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 把x分解成整数和分数两部分，每部分都和x有着相同的符号，整数部分被保存在ip中，分数部分由函数返回</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> mul(M, N)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 矩阵M和矩阵N的积，计算方法如下 
 <div style="text-align:center; margin:1em 0em; position:relative; max-width:none; max-height:none; min-width:0px; min-height:0px; width:782.5px"> 
 <span style="display:inline; line-height:normal; font-size:14px; text-align:left; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> mul(M,N)=⎡⎣⎢⎢⎢M11M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44⎤⎦⎥⎥⎥⎡⎣⎢⎢⎢N11N12N12N13N21N22N23N24N31N32N33N34N41N42N43N44⎤⎦⎥⎥⎥<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-2.996em; overflow:hidden; width:0px; height:6.575em; color:rgb(255,255,255)"> 
 </div> </td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> mul(M, v)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 矩阵M和列向量v的积，公式如下 
 <div style="text-align:center; margin:1em 0em; position:relative; max-width:none; max-height:none; min-width:0px; min-height:0px; width:782.5px"> 
 <span style="display:inline; line-height:normal; font-size:14px; text-align:left; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> mul(M,v)=⎡⎣⎢⎢⎢M11M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44⎤⎦⎥⎥⎥⎡⎣⎢⎢⎢v1v2v3v4⎤⎦⎥⎥⎥<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-2.996em; overflow:hidden; width:0px; height:6.575em; color:rgb(255,255,255)"> 
 </div> </td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> mul(v, M)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 行向量v和矩阵M的积，公式如下 
 <div style="text-align:center; margin:1em 0em; position:relative; max-width:none; max-height:none; min-width:0px; min-height:0px; width:782.5px"> 
 <span style="display:inline; line-height:normal; font-size:14px; text-align:left; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> mul(v,M)=[v1v2v3v4]⎡⎣⎢⎢⎢M11M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44⎤⎦⎥⎥⎥<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-2.996em; overflow:hidden; width:0px; height:6.575em; color:rgb(255,255,255)"> 
 </div> </td> 
 </tr> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> noise(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 根据它的参数类型，这个函数可以是一元、二元或三元噪音函数。返回的值在0和1之间，并且通常与给定的输入值一样</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> pow(x, y)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> <span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> xy<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.068em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"> </td> 
 </tr> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> radians(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 函数将角度值转换为弧度值</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> round(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 返回四舍五入值。</td> 
 </tr> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> rsqrt(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> x的平方根的倒数，x必须大于0</td> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> saturate(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 把x限制到[0,1]之间</td> 
 </tr> 
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 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sign(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> x&gt;0<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:1.004em; color:rgb(255,255,255)"> 则返回1；否则返回0</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sin(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 输入参数为弧度，计算正弦值，返回值范围 为[-1,1]</td> 
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 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sincos(float x, out s, out c)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 该函数是同时计算x的sin值和cos值，其中s=sin(x)，c=cos(x)。该函数用于“同时需要计算sin值和cos值的情况”，比分别运算要快很多!</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sinh(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算x的双曲正弦</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> smoothstep(min, max, x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 值x位于min、max区间中。如果x=min，返回0；如果x=max，返回1；如果x在两者之间，按照下列公式返回数据： <span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> −2∗(x−minmax−min<span style="display:inline-block; position:static; border-width:0px 0px 0px 3.401em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px">)3+3∗(x−minmax−min<span style="display:inline-block; position:static; border-width:0px 0px 0px 3.401em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:0.003em; overflow:hidden; width:0px; height:1.25px">)2<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.568em; overflow:hidden; width:0px; height:1.789em; color:rgb(255,255,255)"> </td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> step(a, x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 如果<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> x&lt;a<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.139em; overflow:hidden; width:0px; height:0.861em; color:rgb(255,255,255)"> ，返回0；否则，返回1</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> sqrt(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 求x的平方根，<span style="display:inline; line-height:normal; font-size:14px; word-spacing:normal; word-wrap:normal; white-space:nowrap; float:none; direction:ltr; max-width:none; max-height:none; min-width:0px; min-height:0px; border:0px; padding:0px; margin:0px"> x<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.579em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.055em; overflow:hidden; width:0px; height:1.25px">√<span style="display:inline-block; position:static; border-width:0px 0px 0px 0.004em; border-left-style:solid; border-color:initial; padding:0px; margin:0px; vertical-align:-0.425em; overflow:hidden; width:0px; height:1.361em; color:rgb(255,255,255)"> ，x必须大于0</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> tan(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算x正切值</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> tanh(x)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 计算x的双曲线切线</td> 
 </tr> 
 <tr style=""> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> transpose(M)</td> 
 <td align="left" style="padding:8px; line-height:20px; vertical-align:top; border:1px solid rgb(238,238,238)"> 矩阵M的转置矩阵 如果M是一个AxB矩阵，M的转置是一个BxA矩阵，它的第一列是M的第一行，第二列是M的第二行，第三列是M的第三行，等等</td> 
 </tr> 
 </tbody> 
</table>

> ### （2）几何函数 ###

> ### （3）纹理映射函数 ###

在这个表中，每个函数第二个参数的名字指明了在执行纹理查询的时候，它的值是如果被使用的:

*  s表示这是一个一元、二元或三元纹理坐标。
 *  z表示这是一个用来进行阴影贴图查找的深度比较值。
 *  q表示这是一个透视值，在进行纹理查找之前，它被用来除以纹理坐标（s）。

当你使用的纹理函数允许你指定一个深度比较值的时候，与之相关联的纹理单元必须被设置成深度比较纹理。否则，深度比较实际上不会被执行。

> ### （4）偏导函数 ###

> ### （5）调试函数 ###

[http_blog.csdn.net_lcbcsdn_article_details_46848125]: http://blog.csdn.net/lcbcsdn/article/details/46848125