数学

介绍

The C++ standard library provides basic math functionality through {code}, which is supported in VEXcode IQ (2nd gen). These functions let you perform common mathematical operations such as trigonometry, rounding, exponentiation, and more.

使用它们来计算位置、角度、距离，或执行度数和弧度之间的转换。

以下是可用的数学函数、常量和实用程序的列表：

常见数学函数 – 常见数学工具。

• abs – Returns the absolute value of a number.

• fmin – Returns the smallest of the input values.

• fmax – Returns the largest of the input values.

• pow – Raises a number to a power.

Constants – Predefined values from {code}.

• M_PI – The constant π (pi).

• M_E – Euler’s number, base of the natural log.

三角学——计算角度和边之间的关系。

• sin – Sine of an angle in radians.

• cos – Cosine of an angle in radians.

• tan – Tangent of an angle in radians.

• atan – Arctangent of a value in radians.

• atan2 – Arctangent of y/x in radians, considering the quadrant.

• asin – Arcsine of a value in radians.

• acos – Arccosine of a value in radians.

舍入和绝对值——调整精度或方向。

• ceil – Rounds up to the nearest integer.

• floor – Rounds down to the nearest integer.

• trunc – Removes the decimal portion.

指数和对数——幂、根和对数计算。

• sqrt – Returns the square root.

• exp – Calculates e to the power of x.

• log – Natural logarithm (base e).

• log10 – Base-10 logarithm.

浮点运算——检查或分解浮点值。

• fmod – Remainder with sign of the dividend.

• copysign – Returns a value with the sign of another.

常见数学函数

abs

abs returns the absolute value of a number, removing any negative sign.

Usage:
abs(x)

范围	描述
x	整数或浮点数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Display the absolute value of -10
  Brain.Screen.print("%d", abs(-10));

  // Output: 10
}

fmin

fmin returns the lower of two values as a float.

Usage:
fmin(value1, value2)

范围	描述
value1	要比较的第一个值。
value2	要比较的第二个值。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Display the lower of two values
  Brain.Screen.print("%f", fmin(7, 4));

  // Output: 4.000000
}

fmax

fmax returns the higher of two values as a float.

Usage:
fmax(value1, value2)

范围	描述
value1	要比较的第一个值。
value2	要比较的第二个值。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Display the higher of two values
  Brain.Screen.print("%f", fmax(7, 4));

  // Output: 7.000000
}

pow

pow returns a number raised to a power as a float.

Usage:
pow(base, exponent)

范围	描述
base	基数。
exponent	指数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Display the lower of two values
  Brain.Screen.print("%f", pow(2, 3));

  // Output: 8.000000
}

常量

常量是预定义的值，在项目执行过程中保持不变。它们可以在计算中使用，无需任何定义或赋值。

M_PI

M_PI gives the mathematical constant π, the ratio of a circle’s circumference to its diameter.

Usage:
M_PI

int main() {
  vexcodeInit();

  // Calculate the area of a circle with radius 5
  double area = M_PI * 5 * 5;

  Brain.Screen.print("%f", area);  
  
  // Output: 78.539816
}

M_E

M_E gives the base of the natural logarithm.

Usage:
M_E

int main() {
  vexcodeInit();

  // Calculate e raised to the power of 2
  double result = pow(M_E, 2);

  Brain.Screen.print("%f", result);  
  
  // Output: 7.389056
}

三角学

sin

sin calculates the sine of an angle in radians and returns a float.

Usage:
sin(x)

范围	描述
x	表示弧度角的浮点数或整数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();

  // Convert 30 degrees to radians
  double radians = 30 * M_PI / 180.0;

  // Display the sine of 30 degrees
  Brain.Screen.print("%f", sin(radians));

  // Output: 0.500000
}

cos

cos calculates the cosine of an angle in radians and returns a float.

Usage:
sin(x)

范围	描述
x	表示弧度角的浮点数或整数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();

  // Convert 60 degrees to radians
  double radians = 60 * M_PI / 180.0;

  // Display the cosine of 60 degrees
  Brain.Screen.print("%f", cos(radians));

  // Output: 0.500000
}

tan

tan calculates the tangent of an angle in radians and returns a float.

Usage:
tan(x)

范围	描述
x	表示弧度角的浮点数或整数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();

  // Convert 45 degrees to radians
  double radians = 45 * M_PI / 180.0;

  // Compute tangent of 45 degrees
  Brain.Screen.print("%f", tan(radians));

  // Output: 1.000000
}

atan

atan calculates the inverse tangent (arc tangent) of a number and returns a float representing the angle in radians.

Usage:
atan(x)

范围	描述
x	表示弧度角的浮点数或整数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();

  // Calculate the arc tangent of 1 in degrees
  double degrees = atan(1.0) * 180.0 / M_PI;

  Brain.Screen.print("%f", degrees);

  // Output: 45.000000
}

atan2

atan2 calculates the principal value of the inverse tangent of y/x and returns a float representing the angle in radians.

Usage:
atan2(y, x)

范围	描述
y	表示 y 坐标的浮点数或整数。
x	表示 x 坐标的浮点数或整数。

int main() {
  vexcodeInit();

  // Calculate the inverse tangent of 1/1 in degrees
  double degrees = atan2(1.0, 1.0) * 180.0 / M_PI;

  Brain.Screen.print("%f", degrees);

  // Output: 45.000000
}

asin

asin calculates the inverse sine (arc sine) of a number and returns a float representing the angle in radians.

Usage:
asin(x)

范围	描述
x	-1 到 1 之间的浮点数或整数。

int main() {
  vexcodeInit();

  // Calculate the arc sine of 0.5 in degrees
  double degrees = asin(0.5) * 180.0 / M_PI;

  Brain.Screen.print("%f", degrees);
  
  // Output: 30.000000
}

acos

acos calculates the inverse cosine (arc cosine) of a number and returns a float representing the angle in radians.

Usage:
acos(x)

范围	描述
x	-1 到 1 之间的浮点数或整数。

int main() {
  vexcodeInit();

  // Calculate the arc cosine of 0.5 in degrees
  double degrees = acos(0.5) * 180.0 / M_PI;

  Brain.Screen.print("%f", degrees);  
  
  // Output: 60.000000
}

四舍五入和绝对值

ceil

ceil returns a number rounded up as a float.

Usage:
ceil(x)

范围	描述
x	需要向上舍入的浮点数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Round up 9.7
  Brain.Screen.print("%f", ceil(9.7));

  // Output: 10.000000
}

floor

floor returns a number rounded down as a float.

Usage:
floor(x)

范围	描述
x	要向下舍入的浮点数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Round down 9.7
  Brain.Screen.print("%f", floor(9.7));

  // Output: 9.000000
}

trunc

trunc returns a number as a float, with its decimal portion set to zero.

Usage:
trunc(x)

范围	描述
x	要截断的浮点数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Truncate 9.7
  Brain.Screen.print("%f", trunc(9.7));

  // Output: 9.000000
}

指数和对数

sqrt

sqrt returns the square root of a number as a float.

Usage:
sqrt(x)

范围	描述
x	非负浮点数或整数。

int main() {
  // Initializing Robot Configuration. DO NOT REMOVE!
  vexcodeInit();
  // Display the square root of 121
  Brain.Screen.print("%f", sqrt(121));

  // Output: 11.000000
}

exp

exp calculates the exponential of a number and returns a float.

Usage:
exp(x)

范围	描述
x	浮点数或整数。

int main() {
  vexcodeInit();

  // Calculate e raised to the power of 1
  double result = exp(1);

  Brain.Screen.print("%f", result);
  
  // Output: 2.718282
}

log

log calculates the natural logarithm of a number and returns a float.

Usage:
log(x)

范围	描述
x	正浮点数或整数。

int main() {
  vexcodeInit();

  // Calculate the natural logarithm (base e) of 7.389056
  double result = log(M_E);

  Brain.Screen.print("%f", result);  
  
  // Output: 1.000000
}

log10

log10 calculates the base-10 logarithm of a number and returns a float.

Usage:
math.log10(x)

范围	描述
x	正浮点数或整数。

int main() {
  vexcodeInit();

  // Calculate the base-10 logarithm of 1000
  double result = log10(1000);

  Brain.Screen.print("%f", result);  
  
  // Output: 3.000000
}

浮点运算

fmod

fmod returns the remainder of division while keeping the sign of the dividend (x).

Usage:
fmod(x, y)

范围	描述
x	股息。
y	除数。

int main() {
  vexcodeInit();

  // Calculate remainder of 10 / -3
  // that preserves the sign of 10
  double result = fmod(10.0, -3.0);

  Brain.Screen.print("%f", result);  
  
  // Output: 1.000000
}

copysign

copysign returns x with the sign of y.

Usage:
math.copysign(x, y)

范围	描述
x	要修改的值。
y	其符号将被复制的值。

int main() {
  vexcodeInit();

  // Return -10 with the sign of 3 (positive)
  double result = copysign(10, -3);

  Brain.Screen.print("%f", result);  
  
  // Output: -10.000000
}