Awakening Elementary School System in University

Tao Wei and Luo Qin’s eyes were fixed on Chen Lin, a mix of tension and anticipation in their gazes.

Fan Jianjun, however, leaned back in his chair and let out a long sigh.

He had discussed this problem with countless domestic experts and scholars, but none had ever provided a satisfactory answer.

Sun Yu sat to the side, completely lost. He recognized each word individually, but strung together, they made no sense to him at all.

The only thing he could do, seeing that Chen Lin didn’t seem inclined to refuse, was to quickly take the hint. He turned, grabbed a fresh stack of A4 scratch paper and a gel pen from his own desk, and placed them in front of Chen Lin.

Shen Yan, however, had taken out her notebook the moment Fan Jianjun began his explanation. She listened and jotted down notes at a furious pace, her clear eyes shining with intense concentration and thought.

This problem was also far beyond her own level, but the optimization theory and Differential Geometry knowledge involved gave her the faint sense that she was touching upon a brand new, far more expansive world of mathematics.

Chen Lin listened quietly to Fan Jianjun’s entire explanation, then glanced down at the dense collection of formulas and diagrams on Luo Qin’s laptop. Throughout it all, his expression remained unchanged, perfectly calm.

In his mind, Little Mathematician was already firing on all cylinders.

B-spline curves, S-shaped velocity curves, nonlinear programming (NLP), quadratically constrained quadratic programming (QCQP)... Countless related mathematical tools and theoretical models surged forth like a tide. Then, with unimaginable efficiency, the system swiftly filtered, reorganized, and optimized them, ultimately constructing a logically perfect framework.

He looked up and gave Fan Jianjun a polite smile.

"I understand."

Then, he picked up the pen on the table and said to Tao Wei’s group, "This might take me a while. Please, feel free to take a break."

"..."

The entire conference table was plunged into a dead silence.

The smile on Tao Wei’s face froze.

Luo Qin’s mouth fell slightly agape, and he forgot to close it.

Even Fan Jianjun, who had just finished his explanation and thought he could finally relax a little, shot bolt upright in his chair. His eyes were wide, and utter disbelief was written all over his face.

"W-wait!" Fan Jianjun’s voice stuttered. "President... President Chen, you understand already? Is there... nothing else you need to ask? For example, the specific forms of the dynamic constraints? Or the details of the path parameterization?"

He simply couldn’t believe his ears.

Just clearly explaining the background and constraints for this problem had taken him nearly five minutes.

Any other expert encountering this field for the first time, even a leading figure, would have needed at least half an hour—if not longer—to digest the information, ask questions, and hash out every last detail before daring to claim they "understood."

And yet this young man before him claimed to understand after hearing it just once?

This was beyond the scope of genius. This was simply monstrous!

Facing their shocked expressions, as if they had just seen a ghost, Chen Lin simply smiled, his tone as calm and nonchalant as ever.

"Engineer Fan’s explanation was very clear. You touched upon every key point, so I have no further questions."

With that, he paid them no more mind, lowered his head, and focused his full attention on the pristine sheet of scratch paper before him.

Tao Wei, Fan Jianjun, and Luo Qin looked at one another, each seeing the same expression of shock and bewilderment reflected in the others’ eyes.

In the end, Tao Wei was the first to react. He gave Fan Jianjun and Luo Qin a meaningful look, and the three of them rose from their seats in unison. Then, they tiptoed over to stand behind Chen Lin, forming a semicircle around him.

Even Shen Yan, unable to contain her curiosity, quietly came over. She stood at the outer edge of the group, rising onto her tiptoes to try and get a look.

All four of them held their breath, their gazes riveted on the every movement of his pen.

Chen Lin’s pen touched the paper.

SCRATCH... SCRATCH...

The crisp, rhythmic sound of the pen was the only thing that could be heard.

At first, Fan Jianjun’s expression was one of scrutiny.

When he saw Chen Lin unhesitatingly choose Non-Uniform Rational B-Splines (NURBS) to parameterize the tool path, he nodded in approval.

This was standard industry practice. While not surprising, it proved Chen Lin knew what he was doing and wasn’t just making things up.

But then, his brow furrowed slightly.

Instead of using the conventional, simpler method of treating the discrete points directly as interpolation or approximation points, Chen Lin took a different approach to the geometric constraints. He introduced an auxiliary variable based on "chord length parameterization," cleverly converting the discrete geometric constraints into a quadratic programming problem for the NURBS control points.

’This step is ingenious!’

Fan Jianjun’s expression grew serious.

And as Chen Lin began to tackle the most central and difficult part of the problem—the "joint dynamic constraints"—Fan Jianjun found his own breathing had quickened without him realizing it.

He saw that Chen Lin wasn’t attempting to separate the path and velocity planning into a multi-step solution like their team had. Instead, from the very beginning, he treated both as a single, unified whole.

He directly defined the path’s geometric parameters (the NURBS control points) and the motion profile’s time parameters (the key time nodes of the S-shaped velocity curve) as the decision variables for the final optimization problem!