“Between every two points lies a story not of straight lines, but of gentle curves where truth is revealed in the transitions.” – MJ Martin
During the 1980s, I was involved in a lot of the early days of computer generated graphics and animation projects for Canadian broadcasters. It was an amazing time due to all of the incredible innovations being developed 40+ years ago.
We were just beginning the global transformation from analog film stop-frame to digital animation.
One project of note, was the BCTV broadcast studio built for, and on the site of Expo 86 in Vancouver. We used an innovative graphic creation platform from Aurora Graphics, they were located in San Francisco and had spun out of the gaming innovator, Atari. Video games were also just transitioning from humble garage startups to real companies with actual offices. The Aurora Graphics system was an incredible early days creative platform long before Photoshop and Illustrator came to the market. It set the standards that are still used today.
Of course, it was just a tool, albeit a fancy one. It needed talented creative people like BCTV’s Creative Director Bob York to bring the content to life.
Aurora did key frame animation years before anyone else. With their systems, genius artists like Bob could create stunning digitally animated graphic sequences. Before Aurora, this sort of work had to be done in stop-frame film animation and hand-drawn pictures. The biggest advantages of the transformation to digital were the increased speed to create output, image quality, cost savings, and artist creative control for repeatable and flexible animations.
One advanced attribute of their system was the early use of splines.
What Is a Spline
A spline (derived from Space-Lines), in its simplest form, is a mathematical way of drawing a smooth curve through a set of points. The word comes from flexible strips of wood once used by shipbuilders and draftsmen to trace elegant curves across fixed pegs. In modern computing, splines serve the same purpose, but instead of wood and nails, they rely on equations to connect data points smoothly. Whether in animation, engineering design, or data visualization, splines help transform discrete measurements into continuous, flowing shapes that are easier to interpret and use.
Understanding the Kochanek–Bartels Spline
The Kochanek–Bartels spline is a specific type of spline that adds three controls at each point along the curve. These controls are called tension, continuity, and bias. Tension determines how tight or loose the curve bends, like pulling a rope taut or letting it sag. Continuity controls how smoothly the curve transitions through a point, similar to whether a road has a gentle bend or a sudden kink. Bias influences the direction of the curve as it enters and exits a point, much like leaning into a turn when riding a bicycle. Together, these three parameters give precise control over the shape and behaviour of the curve.
The Canadian Connection
It was invented by Dr. Doris Kochanek of National Film Board of Canada and Dr. Richard Bartels of University of Waterloo, both in Canada, to automate the process of creating the effect desired by the animator for interpolated motion between key frames in computer animation, reducing the need to input additional information
A Brief History
The concept emerged in the early days of computer animation in the 1980s, when researchers sought better ways to control motion between keyframes. Traditional splines produced smooth results but offered limited artistic control. The Kochanek–Bartels formulation extended earlier Hermite and cardinal splines by allowing each keyframe to influence the motion more expressively. This made it valuable in animation systems where timing and motion nuance were critical.
Modern Alternatives and Industry Shift
Over time, however, the spline became less common in everyday workflows. Its flexibility came at the cost of complexity, requiring users to manage three parameters at every point. As software evolved, simpler and more intuitive approaches gained popularity. Cubic Bézier curves became the standard in animation tools because they provide visual handles that are easier to manipulate. In engineering and modelling, B splines and NURBS offered stable and scalable solutions. Catmull–Rom splines also became widely used for path interpolation because they pass through points naturally without requiring extra tuning. These alternatives did not replace the Kochanek–Bartels spline entirely, but they reduced its prominence by offering a better balance between control and usability.
Application in AMI for Smart Meters
In the context of Advanced Metering Infrastructure for smart meters, splines play a different but equally important role. AMI systems collect large volumes of time series data, such as water flow, gas consumption, or electrical load. These readings often arrive at discrete intervals, yet operators need to understand trends as continuous behaviour. A spline can be used to interpolate between readings, smoothing the data to reveal patterns such as gradual leaks, demand spikes, or system anomalies. The Kochanek–Bartels spline, with its ability to control curvature and direction, can be particularly useful when modelling how consumption changes over time, especially when transitions are not uniform.
A Simple Analogy for Everyday Understanding
A simple way to understand this is to imagine plotting daily water usage as dots on a graph. Connecting those dots with straight lines produces a jagged path that may exaggerate abrupt changes. Using a spline is like replacing those straight lines with a flexible curve that flows naturally between points. The Kochanek–Bartels version lets the analyst decide whether the curve should hug the points tightly, glide smoothly, or favour one direction of change over another. In AMI systems, this can help distinguish between normal consumption patterns and subtle indicators of leakage or operational inefficiency.
Summary
In summary, the Kochanek–Bartels spline remains a powerful mathematical tool, even if it is no longer the default choice in most software. Its strength lies in its fine control over how curves behave, making it valuable in specialized applications where nuance matters. While modern alternatives have simplified the user experience, the underlying principles of splines continue to shape how data, motion, and systems are understood across industries, including the evolving landscape of smart metering.
About the Author:
Michael Martin is the Vice President of Technology with Metercor Inc., a Smart Meter, IoT, and Smart City systems integrator based in Canada. He has more than 40 years of experience in systems design for applications that use broadband networks, optical fibre, wireless, and digital communications technologies. He is a business and technology consultant. He was a senior executive consultant for 15 years with IBM, where he worked in the GBS Global Center of Competency for Energy and Utilities and the GTS Global Center of Excellence for Energy and Utilities. He is a founding partner and President of MICAN Communications and before that was President of Comlink Systems Limited and Ensat Broadcast Services, Inc., both divisions of Cygnal Technologies Corporation (CYN: TSX).
Martin served on the Board of Directors for TeraGo Inc (TGO: TSX) and on the Board of Directors for Avante Logixx Inc. (XX: TSX.V). He has served as a Member, SCC ISO-IEC JTC 1/SC-41 – Internet of Things and related technologies, ISO – International Organization for Standardization, and as a member of the NIST SP 500-325 Fog Computing Conceptual Model, National Institute of Standards and Technology. He served on the Board of Governors of the University of Ontario Institute of Technology (UOIT) [now Ontario Tech University] and on the Board of Advisers of five different Colleges in Ontario – Centennial College, Humber College, George Brown College, Durham College, Ryerson Polytechnic University [now Toronto Metropolitan University]. For 16 years he served on the Board of the Society of Motion Picture and Television Engineers (SMPTE), Toronto Section.
He holds three master’s degrees – in business (MBA), communication (MA), and education (MEd). As well, he has three undergraduate diplomas and seven certifications in business, computer programming, internetworking, project management, media, photography, and communication technology. He has completed over 80 next generation MOOC (Massive Open Online Courses) [aka Micro Learning] continuous education programs in a wide variety of topics, including: Economics, Python Programming, Internet of Things, Cloud, Artificial Intelligence and Cognitive systems, Blockchain, Agile, Big Data, Design Thinking, Security, Indigenous Canada awareness, and more.