Intuitive Mapping in Arduino: Simplifying Numeric Range Conversion

Introduction:

Mapping numeric ranges onto one another is a common task in Arduino projects. Often, the mathematical formulas involved can be daunting, leading to confusion and errors. In this blog post, we will explore an intuitive approach to solve this problem without delving into complex math equations. By breaking down the problem into simpler components and utilizing basic scaling principles, we can achieve accurate and straightforward results.

Simplifying the Mapping Process: Let’s set aside the intricate math and approach the problem intuitively. Our goal is to map input numbers in the range [input_start, input_end] to the output range [output_start, output_end]. By scaling the values appropriately, we can achieve the desired mapping.

First, we can reduce the problem to a simpler scenario. If we want to map numbers from [0, x] to [0, y], we can scale the input values by a factor of y/x. This means that 0 will still map to 0, x will map to y, and any value t will map to (y/x)*t.

Applying the Simplified Approach: Let’s apply the simplified approach to solve your mapping problem. We will use the following variables: input_start, input_end, output_start, output_end, input, and output.

1. Determine the equivalent ranges:
   • The input range [input_start, input_end] is equivalent to [0, r], where r = input_end - input_start.
   • The output range [output_start, output_end] is equivalent to [0, R], where R = output_end - output_start.
2. Calculate the scaled input value:
   • An input value of input is equivalent to x = input - input_start in the simplified range.
3. Map the scaled input value to the output range:
   • Apply the formula y = (R/r)*x to scale the input value.
   • Translate the scaled value y back to the original output range by adding output_start: output = output_start + y.

The Final Formula: Based on the above steps, we can now derive the final formula for mapping the numeric range:

output = output_start + ((output_end - output_start) / (input_end - input_start)) * (input - input_start)

Alternatively, you can use the following code in your Arduino sketch:

double slope = 1.0 * (output_end - output_start) / (input_end - input_start);
output = output_start + slope * (input - input_start);

To obtain more accurate results, especially when dealing with fractional values, consider using floating-point calculations and rounding. You can implement a simple rounding function as shown below:

#include <math.h>

double round(double d) {
    return floor(d + 0.5);
}

output = output_start + round(slope * (input - input_start));

What is the difference between Arduino map() function and the above approach?

The main difference between the Arduino map() function and the above Mapping approach is the level of flexibility and customization they offer.

1. Linear vs. Custom Mapping: The Arduino map() function performs linear mapping, assuming a direct proportional relationship between the input and output ranges. It provides a quick and easy way to map values in a linear fashion. On the other hand, the above approach allows for more flexibility and customization. It allows you to define the input and output ranges, enabling non-linear mappings or more complex transformations.
2. Input and Output Range Limitations: The Arduino map() function operates on integer values and has a limited range. It accepts input and output values within the range of -32,768 to 32,767, as it uses 16-bit integers. In contrast, this approach does not have these limitations. It can work with a wider range of input and output values, including floating-point numbers, by using appropriate data types and calculations.
3. Precision and Error Handling: The Arduino map() function performs integer arithmetic, which may lead to loss of precision when dealing with floating-point values. In contrast, the above approach allows for floating-point calculations, providing higher precision when needed. Additionally, this approach provides an opportunity for error handling and validation by checking the input values before performing the mapping calculation.
4. Processing Overhead: The Arduino map() function involves several mathematical operations, including subtraction, multiplication, and division. While it is generally efficient, the additional computational overhead may be a concern in time-sensitive applications or projects with limited computing resources. The “Intuitive Mapping in Arduino” approach offers more control over the calculations performed, allowing you to optimize for performance if necessary.

Conclusion:

In summary, the Arduino map() function is a quick and easy way to perform linear mapping operations in Arduino projects with limited precision and customization. The “Intuitive Mapping in Arduino” approach provides more flexibility, allowing for custom mappings, increased precision with floating-point calculations, error handling, and the ability to handle a wider range of input and output values. Depending on the project requirements, one approach may be more suitable than the other.