217 lines
5.6 KiB
Python
217 lines
5.6 KiB
Python
"""
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流体动力学插件数学工具模块
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提供流体模拟所需的数学计算功能
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"""
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import math
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from panda3d.core import Vec3, Point3
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class FluidMathUtils:
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"""
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流体数学工具类
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提供流体模拟所需的数学计算功能
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"""
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@staticmethod
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def dot_product(a, b):
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"""
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计算两个向量的点积
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Args:
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a (Vec3): 向量a
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b (Vec3): 向量b
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Returns:
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float: 点积结果
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"""
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return a.dot(b)
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@staticmethod
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def cross_product(a, b):
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"""
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计算两个向量的叉积
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Args:
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a (Vec3): 向量a
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b (Vec3): 向量b
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Returns:
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Vec3: 叉积结果
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"""
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return a.cross(b)
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@staticmethod
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def vector_length(v):
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"""
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计算向量长度
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Args:
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v (Vec3): 向量
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Returns:
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float: 向量长度
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"""
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return v.length()
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@staticmethod
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def normalize_vector(v):
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"""
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归一化向量
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Args:
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v (Vec3): 向量
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Returns:
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Vec3: 归一化后的向量
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"""
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if v.length() > 0:
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return v.normalized()
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return Vec3(0, 0, 0)
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@staticmethod
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def distance(a, b):
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"""
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计算两点间距离
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Args:
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a (Point3): 点a
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b (Point3): 点b
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Returns:
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float: 距离
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"""
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return (a - b).length()
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@staticmethod
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def interpolate(a, b, t):
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"""
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线性插值
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Args:
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a (float): 起始值
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b (float): 终止值
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t (float): 插值参数 (0-1)
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Returns:
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float: 插值结果
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"""
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return a + (b - a) * t
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@staticmethod
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def clamp(value, min_val, max_val):
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"""
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限制值在指定范围内
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Args:
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value (float): 值
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min_val (float): 最小值
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max_val (float): 最大值
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Returns:
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float: 限制后的值
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"""
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return max(min_val, min(max_val, value))
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@staticmethod
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def smoothstep(edge0, edge1, x):
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"""
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平滑步进函数
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Args:
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edge0 (float): 起始边缘
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edge1 (float): 终止边缘
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x (float): 输入值
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Returns:
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float: 平滑步进结果
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"""
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t = FluidMathUtils.clamp((x - edge0) / (edge1 - edge0), 0.0, 1.0)
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return t * t * (3.0 - 2.0 * t)
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@staticmethod
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def calculate_pressure(density, rest_density, gas_constant):
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"""
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计算压力（状态方程）
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Args:
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density (float): 当前密度
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rest_density (float): 静止密度
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gas_constant (float): 气体常数
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Returns:
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float: 压力值
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"""
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# 简单的状态方程: P = k * (ρ - ρ₀)
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return gas_constant * (density - rest_density)
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@staticmethod
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def calculate_viscosity_force(velocity_diff, viscosity, distance, radius):
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"""
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计算粘性力
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Args:
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velocity_diff (Vec3): 速度差
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viscosity (float): 粘度
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distance (float): 距离
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radius (float): 影响半径
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Returns:
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Vec3: 粘性力
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"""
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# 基于距离的权重
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weight = 1.0 - distance / radius if distance < radius else 0.0
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# 粘性力与速度差和粘度成正比
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return velocity_diff * viscosity * weight
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@staticmethod
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def calculate_surface_tension_force(normal, surface_tension, curvature):
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"""
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计算表面张力力
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Args:
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normal (Vec3): 表面法线
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surface_tension (float): 表面张力系数
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curvature (float): 曲率
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Returns:
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Vec3: 表面张力力
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"""
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# 表面张力力与曲率和法线方向有关
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return normal * surface_tension * curvature
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@staticmethod
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def calculate_buoyancy(density_diff, gravity):
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"""
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计算浮力
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Args:
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density_diff (float): 密度差
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gravity (Vec3): 重力向量
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Returns:
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Vec3: 浮力
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"""
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# 浮力与密度差和重力成正比
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return gravity * density_diff
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@staticmethod
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def calculate_drag_force(velocity, drag_coefficient, fluid_density, area):
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"""
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计算阻力
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Args:
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velocity (Vec3): 速度向量
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drag_coefficient (float): 阻力系数
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fluid_density (float): 流体密度
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area (float): 参考面积
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Returns:
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Vec3: 阻力向量
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"""
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speed = velocity.length()
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if speed > 0:
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# 阻力公式: F = 0.5 * ρ * v² * Cd * A
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drag_magnitude = 0.5 * fluid_density * speed * speed * drag_coefficient * area
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drag_direction = -velocity.normalized()
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return drag_direction * drag_magnitude
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return Vec3(0, 0, 0) |