# [Math]Arithmetic Formula Collections

Mathematics https://keisan.casio.com/menu/system/000000000250 Calcuate distance from foot of perpendicular to line https://math.stackexchange.com/questions/33868/foot-of-perpendicular-to-line How do you find the distance from a point to a plane? https://math.stackexchange.com/questions/88392/how-do-you-find-the-distance-from-a-point-to-a-plane How to find the equation of a plane using three non-collinear points https://www.maplesoft.com/support/help/maple/view.aspx?path=MathApps%2FEquationofaPlane3Points Find the equation of the plane knowing that it passes through 3 points https://math.stackexchange.com/questions/1156983/find-the-equation-of-the-plane-knowing-that-it-passes-through-3-points Find plane by normal and instance point + distance between origin and plane https://math.stackexchange.com/questions/752252/find-plane-by-normal-and-instance-point-distance-between-origin-and-plane

# [Math]Parabola movement

keywords：抛物运动、Parabola、重力加速度、Gravitational Speed 、UE4 implement. header AStaticMeshActor* TestCube = nullptr; //throw speed UPROPERTY(EditDefaultsOnly) FVector StartForce = FVector(100.f, 100.f, 2000.f); //gravitational acceleration float GravityAcclerator = -980.f; //accumulated movtion time float AccumulateTime = 0.f; cpp void ATestTPGameMode::StartPlay() { Super::StartPlay(); //finding the Actor in scene. for (TActorIterator<AStaticMeshActor> Iter(GetWorld()); Iter; ++Iter) { if (Iter->GetName() == TEXT("Cube_2")) { TestCube = *Iter; break; } } } void ATestTPGameMode::Tick(float DeltaSeconds) { Super::Tick(DeltaSeconds); AccumulateTime += DeltaSeconds; //calculate gravitational speed in real time.

# [Math]Projectile Motion: Finding the Optimal Launch Angle

If we want to throw a projectile as far as possible, at what angle should it be launched? This paper focuses on how the answer to this question changes depending on the situation. 如果你想尽可能远的抛掷物体，以多大的角度抛出最合适？这篇文章用于分析不同测试环境下而导致的不同答案。 论文地址：Projectile Motion: Finding the Optimal Launch Angle https://www.whitman.edu/Documents/Academics/Mathematics/2016/Henelsmith.pdf UE4实现：如何绕开障碍物并投掷到指定位置 Projectile: How to avoid obstacle & hit target https://www.reddit.com/r/unrealengine/comments/9xfdei/projectile_how_to_avoid_obstacle_hit_target/ 所有的战争都是内战，因为所有的人类都是同胞。——弗朗索瓦·费奈隆（FrancoisFenelon）

# [Math]The Mathematics of the 3D Rotation Matrix

The Mathematics of the 3D Rotation Matrix https://www.fastgraph.com/makegames/3drotation/ How to combine rotation in 2 axis into one matrix http://computergraphics.stackexchange.com/questions/1608/how-to-combine-rotation-in-2-axis-into-one-matrix Rotation matrix https://en.wikipedia.org/wiki/Rotation_matrix 云山苍苍，江水泱泱，先生之风，山高水长。---范仲淹《严先生祠堂记》

To Be Marvelous

Yichang·Hubei