<center>**Hello everyone!**</center>

How is everything going? Hope you're a having a great time during these summer days. Time to relax and enjoy the simple things in life; our friends and families. I am privileged to live by the sea, so I have been taking advantage of this lately. Everything is great and I felt refreshed, so I thought it's time to share another part of this series with you.  But I'm always in a rush, so I don't mean to waste your time. Let's do this!

**As promised in a previous [Cartography post](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-statistical-surface-and-linear-symbols) regarding the techniques and methods followed in order to represent the statistical surface with the utilization of linear symbols, this is the twentieth part of this Introduction to Cartography Series.  *A milestone I never thought I would reach!* This time I would like to take the chance to share general information regarding isarithmic mapping. We will talk about the methods followed and the tools utilized in the projection of 3D surfaces. We will also talk about the two different categories of chracteristic value variables regarding point data, so stay focused!**

This is a personal note for those of you who are new to my blog; you should always keep in mind that this is an introductory series about Cartography, which is the art and science of creating accurate 2D depictions of our 3D world. This means that I will be presenting broad information with a pinch of humour, so that nobody gets too bored reading this blog. There's always a high chance of learning a thing or two by reading through this series' episodes, so stay tuned!

![abstract-1278061_960_720.jpg](https://cdn.steemitimages.com/DQmctvcwRkKTM3JL49whUUxF8vVWxqCnRuSsw4hdwYLFd46/abstract-1278061_960_720.jpg)
<center>*Image Source: [pixabay.com](https://pixabay.com/el/%CE%B1%CF%86%CE%B7%CF%81%CE%B7%CE%BC%CE%AD%CE%BD%CE%B7-%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%B9%CE%BA%CE%AC-%CE%BA%CF%8C%CF%83%CE%BC%CE%BF-%CF%87%CE%AC%CF%81%CF%84%CE%B7%CF%82-1278061/)([CC0 Creative Commons](https://pixabay.com/el/service/terms/#usage) Author: [Insspirito](https://pixabay.com/el/users/insspirito-1851261/))*</center>

# Symbolization Problems
As explained multiple times in the previous episodes of this ***Introduction to Cartography*** series, the whole process of map symbolization is a rather complicated task that demands the availability of theoretical knowledge related to various different scientific fields. In the [last episode](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-statistical-surface-and-linear-symbols) of this series I shared broad technical information concerning the symbolization of volumetric data with the utilization of linear symbols. The calculations necessary in order to design the statistical surface for an area of interest with specific dimensions induce the need for the inclusion of all different sorts of spatial information (point, linear, surface). The first two types were the subjects of my last two uploads, which basically means that we are now about to focus on surface data, and therefore talk about the isarithmic method. Bare with me.

All symbolization problems addressed in this blog regarding the calculations necessary for the successful conclusion of the design and construction of the statistical surface, refer to the specific occasion where the existence of volumetric data on a surface of interest of given dimensions has to be represented with the utilization of surface symbols and patterns that are comprised of linear symbols. The creation, utilization, application and appropriate placement of linear symbols and surface symbols that were created with the use of linear elements has always been commonly used by Cartographers in the depiction of volumetric spatial data on surfaces of given location and geometry. This is the hand we were dealt; it is all about making the right use of the available linear elements.

All surface symbols are mainly comprised of linear elements and can easily be perceived as a combination of repetitive linear elements that follow certain rules regarding location, geometry and orientation. All three measurable quantities mentioned are absolutely necessary for the precise description of a geographic entity through the creation of a map. And this is one of the main reasons why specific sorts of symbols refer to certain geometric attributes and represent the frequency of appearance of specific spatial elements. Sets of rules that were developed taking into consideration the way the human sensory system works have been placed in order to make the symbolization of 3D surfaces possible. However it is still a very tough job. Let's see why.

![abstract-1278069_960_720.jpg](https://cdn.steemitimages.com/DQmaCrtSZt8XUJm9ivb73Fr8psycARZnUXNVpswnqb5FJGm/abstract-1278069_960_720.jpg)
<center>*Image Source: [pixabay.com](https://pixabay.com/el/%CE%B1%CF%86%CE%B7%CF%81%CE%B7%CE%BC%CE%AD%CE%BD%CE%B7-%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%B9%CE%BA%CE%AC-%CE%BA%CF%8C%CF%83%CE%BC%CE%BF-%CF%87%CE%AC%CF%81%CF%84%CE%B7%CF%82-1278069/)([CC0 Creative Commons](https://pixabay.com/el/service/terms/#usage) Author: [Insspirito](https://pixabay.com/el/users/insspirito-1851261/))*</center>

# Isarithmic Process
The whole concept of the symbolization process when it comes to the precise representation of 3D surfaces is a rather complicated task. Such a demanding task that the time and effort demanded in order to come up with suitable solutions regarding this issue is much more than what it takes to solve all symbolization problems faced together up until this point. This is a challenge that can thankfully be handled with the utilization of a very useful tool that is known as the Isarithmic Process. The Isarithmic Process is a mathematical tool that is mainly used in two different cases, depending on the spatial characteristics that are studied and measured in each case. Let's take a deeper look at each one of those theoretical situations.

![632px-France_map_Lambert-93-Maximum_altitude.svg.png](https://cdn.steemitimages.com/DQmZLWeooGJLigXAAiu43DJ2yF1JdPndS3KqWhcSPcTHZw3/632px-France_map_Lambert-93-Maximum_altitude.svg.png)
<center>*Maximum Altitude, Map of France 1993 - Hue and saturation used as primary visual variables in order to represent quantitative variations described by an ordinal scale./ Image Source: [commons.wikimedia.org](https://commons.wikimedia.org/wiki/File:France_map_Lambert-93-Maximum_altitude.svg) ([Creative Commons](https://en.wikipedia.org/wiki/Creative_Commons) [Attribution-Share Alike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/deed.en) Author: [Babsy](https://commons.wikimedia.org/wiki/User:Babsy))*</center>

The Isarithmic Process can be a very useful asset when the outter shape of a surface is the main point of interest of a study. Specific geometric attributes are the key variables in this case, which basically means that the volumetric data utilized by Cartographers and Engineers in general refers to certain measurable quantities that are linked to the geometry of our surface of interest. It is also worth noting, even though it should be more than obvious by now, that the dimensions of our area of interest are precisely known. Some of the most significant quantities measured  provide Cartographers with information regarding the orientation of our geographic entities and the slope of the natural terrestrial surface.

![704px-Greece_topo.jpg](https://cdn.steemitimages.com/DQmWtjnWzT5KhSgi5N4JMR8gQjhMgRgSLArzCEGKLKrnsAC/704px-Greece_topo.jpg)
<center>*Topography of Greece, 2006 - Hue used as a primary visual variables in order to represent qualitative variations./ Image Source: [commons.wikimedia.org](https://commons.wikimedia.org/wiki/File:Greece_topo.jpg) ([Creative Commons](https://en.wikipedia.org/wiki/Creative_Commons) [Attribution-Share Alike 3.0 Unported](https://creativecommons.org/licenses/by-sa/3.0/deed.en) Author: [Captain Blood](https://en.wikipedia.org/wiki/User:Captain_Blood))*</center>

There is also another theoretical situation in which the uilization of the Isarithmic Process seems to be the key and is commonly embraced by scientists all over the globe. Needless to say, certain geometric attributes are studied and measured in this case as well, defining the whole model that will be utilized for the extraction of metric information in order to reach safe conclusions. In this scenario, the measurable quantities that are linked to the geometry of our surface of study refer to specific spatial characteristics that describe the values of continuous geographic phenomena in particular. This basically means that the phenomena being studied do follow, and therefore can be described by, a continuous statistical distribution.

![Elevation.jpg](https://cdn.steemitimages.com/DQmT2JbUYmxDjFPR1dvqDfETyyN4jqarSpGjcXBwsudhWBX/Elevation.jpg)
<center>*Global Land & Undersea Elevation - Surface symbols used to depict qualitative variations, hue used as a primary visual variable in order to represent qualitative variations described by an ordinal ratio scale./ Image Source: [commons.wikimedia.org](https://commons.wikimedia.org/wiki/File:Elevation.jpg) ([Public Domain](https://en.wikipedia.org/wiki/Public_domain) Author: [U.S. Government](https://en.wikipedia.org/wiki/Copyright_status_of_work_by_the_U.S._government))*</center>

# Types of Isarithmic Mappings
There are two types of characteristic values; the first category refers to variables that are linked with spatial characteristics that can be represented by point symbols. The atmospheric temperature, the altitude of the natural terrestrial surface or the depth of the seabed (distance from the surface) are just a few examples of measurable quantities that refer to specific points on the natural terrestrial surface. High caution is demanded when making measurements regarding quantities that can be represented by point symbols, mainly due to the fact that even the slightest error could potentially affect the validity of our measurements. Needless to say, this would affect our calculations in return, and therefore downgrade the quality of the end product.

There are significant differences in relation to the previous category of characteristic values, when dealing with characteristic values that do not refer to specific points in space (or on the natural terrestrial surface), and therefore cannot be represented with the utilization of point symbols. Human population per square kilometer, percentage of agricultural surfaces per square kilometer, and ratio of specific kinds of agricultural products per square kilometer are just a few examples of measurable quantities that refer to surfaces of given dimensions on the natural terrestrial surface. In this case, instead of the exact 3D location of an entity, Cartographers utilize and measure surface units. Obviously, the final calculations are highly affected by the precision regarding the observations made. No precision means no quality; Engineers appreciate precision. Thanks for your time!

![800px-Population_density_countries_2017_world_map,_people_per_sq_km.svg.png](https://cdn.steemitimages.com/DQmfQfnUNk5M6ewADHqUmiqjaXcTsb9oLcNARAQpEjLMwS5/800px-Population_density_countries_2017_world_map,_people_per_sq_km.svg.png)
<center>*Population Density, World Map 2017 - Saturation used as a primary visual variable in order to represent quantitative variations described by an ordinal scale./ Image Source: [commons.wikimedia.org](https://commons.wikimedia.org/wiki/File:Population_density_countries_2017_world_map,_people_per_sq_km.svg) ([Creative Commons](https://en.wikipedia.org/wiki/Creative_Commons) [ Attribution-Share Alike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/deed.en) Author: [Ms Sarah Welch](https://commons.wikimedia.org/wiki/User:Ms_Sarah_Welch))*</center>

**Alright eveyrone, that's all for today, thank you for the attention. We have now reached the end of this milestone part of my beloved *Introduction to Cartography* series. Looks like there is a long way to go, even though I never thought I'd reach this point. Please bare with me and sit tight, there is a lot more to learn as we move forward. Make sure to let me know  in the comments below if there are any questions regarding my work. More Engineering stuff regarding Cartography and Geology coming out within the next days, so stay tuned and follow me for more!**

# PREVIOUS PARTS OF THE SERIES:

1. [INTRODUCTION TO CARTOGRAPHY](https://steemit.com/engineering/@lordneroo/introduction-to-cartography)

2. [CLASSIFICATION & BROAD CATEGORIES](https://steemit.com/engineering/@lordneroo/introduction-to-cartography-classification-and-broad-categories)

3. [CARTOGRAPHIC TRANSFORMATIONS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-cartographic-transformations)

4. [CONFORMAL PROJECTIONS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-conformal-projections)

5. [EQUAL AREA PROJECTIONS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-equal-area-projections)

6. [AZIMUTHAL PROJECTIONS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-azimuthal-projections)

7. [SCALE FACTOR & TRANSFORMATION](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-scale-factor-and-transformation)

8. [CARTESIAN COORDINATES & GRID SYSTEMS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-cartesian-coordinates-and-grid-systems)

9. [3D COLOR SPACE](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-3d-color-space)

10. [COLOR SYSTEMS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-color-systems)

11. [COLOR & PATTERN IN SYMBOLIZATION (Part I)](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-color-and-pattern-in-symbolism-part-i)

12. [COLOR & PATTERN IN SYMBOLIZATION (Part II)](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-color-and-pattern-in-symbolism-part-ii)

13. [CARTOGRAPHIC SYMBOLIZATION & VISUAL VARIABLES](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-cartographic-symbolization-and-visual-variables)

14. [SYMBOLIZING POINT DATA](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-symbolizing-point-data)

15. [SYMBOLIZING LINEAR DATA](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-symbolizing-linear-data)

16. [SYMBOLIZING SURFACE DATA](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-symbolizing-surface-data)

17. [SYMBOLIZING VOLUMETRIC DATA](https://steemit.com/steemstem/@lordneroo/introduction-to-cartgoraphy-symbolizing-volumetric-data)

18. [STATISTICAL SURFACE & POINT SYMBOLS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-statistical-surface-and-point-symbols)

19. [STATISTICAL SURFACE & LINEAR SYMBOLS](https://steemit.com/steemstem/@lordneroo/introduction-to-cartography-statistical-surface-and-linear-symbols)

![DQmQPRBLmhWag36FBxYVNJNKZRUsBbpPeZvm7FVixnWVXhk_1680x8400.png](https://steemitimages.com/DQmTjUEWdmEvtQcJMueV3YTGnHVNweSGbfDAAEVnCRGPJm4/DQmQPRBLmhWag36FBxYVNJNKZRUsBbpPeZvm7FVixnWVXhk_1680x8400.png)

**IMAGE SOURCES:**

- [pixabay.com](www.pixabay.com)

- [commons.wikimedia.org](https://commons.wikimedia.org)

**REFERENCES:**

***University Textbooks & Course Lectures:***

- Χαρτογραφία Ι/ Cartography I -TSOULOS(National Technical University of Athens, School of Rural & Surveying Engineering, Course Lecture Notes)

- Χαρτογραφία ΙΙ/ Cartography II - NAKOS(National Technical University of Athens, School of Rural & Surveying Engineering, Course Lecture Notes)

***Internet Links:***

- http://www.geog.ucsb.edu/~kclarke/Geography183/Lecture11.pdf

- https://pubs.usgs.gov/tm/2005/11B01/05tm11b01.html

- https://www.researchgate.net/figure/A-Isarithmic-and-B-contour-line-maps-produced-by-the-study_fig4_257820422

- https://help.rockware.com/rockworks17/WebHelp/maps_2d_symbols.htm

- https://link.springer.com/article/10.1007/BF01939851

- https://prism.ucalgary.ca/bitstream/handle/1880/45758/2001-693-16.pdf?sequence=2&isAllowed=y

![DQma1ThzvUGdpwhn4q4PXX8Qj79r2B7Cz9JTfaAYvGJwMGq_1680x8400.jpg](https://steemitimages.com/DQmcRNxuFypkk58sME7csZre64JWz681HzL2fujgWaHe41m/DQma1ThzvUGdpwhn4q4PXX8Qj79r2B7Cz9JTfaAYvGJwMGq_1680x8400.jpg)

![DQmQPRBLmhWag36FBxYVNJNKZRUsBbpPeZvm7FVixnWVXhk_1680x8400.png](https://steemitimages.com/DQmTjUEWdmEvtQcJMueV3YTGnHVNweSGbfDAAEVnCRGPJm4/DQmQPRBLmhWag36FBxYVNJNKZRUsBbpPeZvm7FVixnWVXhk_1680x8400.png)

<center>**Thank you for your attention!**</center>
<center>**Hope you enjoyed this post and did learn a thing or two.**</center>
<center>**Follow me and stay tuned for more engineering blogs.**</center>

<center>**Highest Regards**</center>
<center>**@lordneroo**</center>